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Ted can dig a hole in 30min, Ed can do it in 40min, how long will it take if they work together?
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- čas přidán 7. 03. 2024
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As soon as they begin they have dug a hole
True! Lol
They didn't say how big the hole was-but I admit it does seem a bit slow to take 30 or 40 min just to begin.😊
Like it!
@@darrylschultz9395 Maybe they really didn't want to be digging and it takes a long time to get the energy up and pull that first shovel full out.
e) A lot longer because they'll be whacking each other with their shovels.
Also - easiest WAY to do this - if you don’t want to add fractions or even figure out which to add - is find a common amount of time that each dig an integer number of holes. Which is 2 hours 4 for one 3 for the other. 7 holes in 120 minutes. 120/7 minutes for both together.
With multiple choice I got it this way:
If they both could dig the hole in 30 minutes, it would take them 15 minutes, together.
If they both could dig the hole in 40 minutes, it would take them 20 minutes, together.
So the answer has to be between 15 and 20 minutes.
15.3 minutes seemed too close to 15, so the only answer left is 17.1. I would have guessed 17.5, but that would have been wrong. Why? I have no clue.
Having forgotten how to do combined work problems 57 years ago (the same year it was taught to me) I would be lost without the multiple choice.
Glad to be re-learning this, though. Maybe it will stick this time. Why bother? I have no clue.
"Why? I have no clue." I'll try to explain why •••
If they dig for 15 minutes, Ted will have dug 1/2 of the hole. And Ed will have dug most but not all of the other half of the hole. •••
If only Ed works to complete the hole, he will finish the entire hole (whole hole?) in 5 additional minutes, for a total time of 20 minutes.
If instead, they both work to dig the rest of the hole, at Ed's rate, they'll finish the hole in 2.5 additional minutes, for a total time of 17.5 minutes.
But Ted digs faster than Ed so they'll finish the hole in slightly less than 2.5 additional minutes, for a total time of slightly less than 17.5 minutes (17.1 minutes).
Not sure how to present this "formally," but here's my logic, for what it's worth.
Ted does 1/30th of the work per minute.
Ed does 1/40th ditto
1/30 + 1/40 = 7/120
So between them they do 7/120th per minute.
The whole hole (sorry!) is obviously 120/120 so we need to find out how many 7's make 120:
120/7 = 17.1 and some change.
Which, thankfully, is one of the choices given, so I think my logic might be air-tight. I'm sure there must be easier ways to approach it though.
My ''logic'' was similiar.
7 holes in 120 minutes = 17.1 minutes per hole
You are right. The concept of rate. this how it should have been explained by the person who created the video - but he clearly danced around it - by giving an equation and then spending time to explain the solving of eq. Also some one in above comments gave an analogy to resistors in circuit - perfect !
I solved before watching the video and had a slightly different approach:
Ted digs a hole in 30mins, Ed digs a hole in 40mins.
Therefore, in 10 mins, Ted digs 1/3 of a hole, and Ed digs 1/4 of a hole
Alternatively, in 1 min, Ted digs 1/30 th of a hole and Ed 1/40 th of a hole
(Also, in 2 mins Ted digs 2/30 th and Ed digs 2/40 th etc)
So therefore, if it takes X mins for both to dig a hole, then X/30 +X/40 =1 (hole)
Solve by multiplying by 4/4 and 3/3 to give a common denominator of 120:
ie 4X/120 + 3X/120 =1
4X + 3X = 120 (ie 120/120=1)
7X=120
Therefore X=120/7=17.14 minutes
Then I watched the video and found the mathematical formula way of doing confusing.
I only watch the video if I can't get it. But that is exceptional...
I didn’t bother with the maths, I just thought « If Ed was as fast as Ted, it would take half the time. Bud Ed is slightly slower, so it will take just over half the time. » For a multiple choice question, you don’t always need maths.
That is true, in this case you don't need math to find the correct answer BECAUSE of the stupid multiple choice. Still I will do the mental job to find out if the correct answer is really correct. Always challenge the teacher !
Wow he goes on and on!
. . . and on and on. He could have explained the whole process in about three minutes, but just constantly repeated himself. 🙄 I won’t be subscribing !! 😁
Same here on and on and on
I was wondering how many project managers were going to look at this & start to figure out if the 2 could fit together in the hole & still get the work done at their regular rate of digging.
You are of course correct,
I guess it has the best chance of working out if the diameter of the hole was on the "large" side, large enough for 2 men to work in at the same time. (And fairly shallow would help too).
Perhaps the better way to consider it is if you just call it "moving dirt":
Ted can move a quantity of dirt (pounds/"yards"³/tons/m³) to a pile in 30 minutes, and Ed can move the dirt in 40 minutes. If they work together •••
@@GFlCh That would have been a good example to use, I agree.
For those who studied circuits, this is very similar to finding the total resistance of resistors in parallel. "The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances."
One can think of each resistor doing its fair portion of work.
good analogy.
Yes, the reciprocal of the sum of the reciprocals of the all the individual resisters in the circuit.
Hi math guy! I usually solve the problems in my head before I watch your videos, and THEN I watch your videos. BUT I did this one differently than you did - I started with x/30+ x/40 =1 hole dug. You are a genius for calling this a hole and not a ditch. LOOK at all the comments! Jeez.
I don't feel rusty for doing it the way I did. What we were looking for was more evident to me from my start.
You started way ahead of where i started. But where I started was easy for me to see in my head.
Depends on when one gets out of the hole and lets the other in to dig for awhile.
Skip the algebra when given 4 choices like these. Somewhere between 15 (2 thirties) and 20 (2 forties). And it would take a 15 and a 16 to be between 15 and 16. So 17.1 is only reasonable one.
This is why multiple choice is stupid, making it a guessing contest in stead of algebra... I appreciate to find the answer with the lowest input of brain power but only as an educated guess to validate the answer from algebra.
When I was 7 or 8 years old, my notorious tease of a father introduced me to the following problem: if one ship can cross the Atlantic in five days, how long would it take two ships to cross the Atlantic?😂
Are they transit ships 😂❤
Your father has a good sense of humor.
What weights more: two pounds of lead or 2 pounds of feathers?
@@panlomito It depends. Are the feathers wet or dry?
@@terry_willis They are soaked...
Hopefully the supervisor didn't get Ed and Ted's work mixed up for hourly pay.
"Before i go off on a tangent" Math pun !!!
I think I can sine off on your comment.
You know what gets in the way of learning math? The human instinct to understand and know how/why things work, like reading a book that concludes eventually. With math there is no conclusion.
With math you only learn small amounts at any one time. You have to be comfortable with the indirect acquisition of a skill by way of a process. Math is the language of the universe. You have to accept that you'll never know math in its entirety.
One of the biggest obstacles in math is learning how to learn math.
You get a conclusion every time you solve a problem
@wlonsdale, but for some people they perceive It an unsatisfying, isolated conclusion for something that isn't tangible.
If you like math, solving problems is satisfying for its own sake and each correct answer, even more so.
If you're mandated to learn algebra, as many students are, you need to focus entirely on learning processes without hoping to see the big picture because there isn't the cliche big picture.
In 40 minutes Ed digs 1 hole and Ted digs 1 1/3 holes. Together, in 40 minutes they dig 2 1/3 holes. 40 / 2 1/3 = 17.14 minutes per hole.
Ted's rate of work is 1/30th hole per minute etc . , combining the two gives T=17.1 min as the solution of
(1/30+1/40) x T =1
I would like to see this type of question in the gcse exam
In the gcse syllabus, work questions are usually of the inverse or direct proportion type.
Time total = T1xT2/T1+T2=17.14
That is the shortest possible answer but for clarity:
Ttotal = ( T1 x T2 ) / ( T1 + T2 ) = ( 30 x 40 ) / ( 30 + 40 ) = 1200 / 70 = 17 1/7 minutes
You're welcome !
Depends on how big the hole is, if they can't both dig at the same time it would probably take longer than 40 minutes.
Tell me why this isn't right: two Ted's would do it in 15 mins. Two Ed's would take 20 mins. So Ted and Ed take 17.5 mins?
2 hours will be the first time that both finish digging a hole together.
Ted will dig 4 and Ed will dig 3 .. which is 7 holes altogether.
1 hole, together, would therefore take 2 hours divided by 7.
120 minutes divided by 7 .. 17.140 minutes .. answer b)
55 minutes, because Ed won't f'n shut-up about what he did on his last vacation to Mexico and Ted's too polite to hit him with his shovel.
b)17.1
There is a well known variation on this problem, nice to work this out:
Alex and Bob can do the job in 2 hours
Alex and Charles can do the job in 3 hours
Bob and Charles can do the job in 4 hours
How many time is needed if they work all together... The answer must be less than 2 hours!
Say working speed of Alex is A, of Bob is B and Charles is C, all in job/hour:
2 . (A+B) = 1 so A+B = 1/2 -> A = 1/2 - B
3 . (A+C) = 1 so A+C = 1/3 -> A = 1/3 - C
4 . (B+C) = 1 so B+C = 1/4 -> B = 1/4 - C
So we have 3 equation with 3 variables that we can solve:
1/2 - B = 1/3 - C so B = C + 1/2 - 1/3 = C + 1/6
1/4 - C = C + 1/6 so 2C = 1/4 - 1/6 = 1/12 -> C = 1/24
Then B = 1/4 - C = 6/24 - 1/24 = 5/24
And A = 1/2 - B = 12/24 - 5/24 = 7/24
Time working together = 1 job / (speed together) = 1 / (A+B+C) = 1 / (7/24 + 5/24 + 1/24) = 1 / (13/24) = 24/13 =
1 11/13 hour and that is 1 hour and 60 . 11/13 minutes = 1 hour, 50 minutes and 46 seconds.
In one minute do together
1/40+1/30=
7/120
The is représente by 1.
1÷7/120
1×120÷7
17.1
The answer is b
Product over the Sum as long as the units are the same
But if Fred shows up and can dig it in 25 minutes you need a different formula.
You seemed to rush that cross multiplication manipulation of the fractions at the end. A bit odd because you spend ages explaining the really obvious bits. But that last bit would be a bit hard to follow for many students and could do with being explained in a bit more detail at a slower pace.
Sir please give us prove of this formula 😢😢
The way you state the problem is ambiguous. The time you gave is If they take turns digging. Not if they work together.
Why wouldnt the LCD for 30 and 40 be 5
Is there a video that explains how you arrived at the formula that you used?
At the title (0:08), my answer is b) 17.1 min.
Ted can did 1 whole hole in 30 minutes.
Ed can dig 3/4 of a hole in the same 30 minutes, since it takes him 40 minutes for a complete hole.
Therefore, working together they could dig 1 3/4, or 7/4 holes in 30 minutes.
So, 30 minutes divided by 1.75 holes per 30 minutes ~ 17.1 minutes for one hole working together.
Great job
I understand this better than the answer of the video
Deu 17,1 min, letra B.
All holes being equal.
And what about elbow space?
I may have known what you ment but the question was terrible. Two people cannot dig a hole at the same time.
You've never been in the Army. 😉
JC… I can’t even take the Mambi pamby voice.
I chose 17.1 without doing the math because it fit the basic math based on the options.
The time has to be close to 30/2! So 17.1.
first of all....
let's express each digger's ability
Ted: 1hole/30min
Ed: 1hole/40min
solving
1st step
Ted: 1hole/30min
=0.033hole/min
Ed: 1hole/40min
=0.025hole/min
Together
=0.033+0.025 hole/min
=0.058hole/min
Resolve:
min/hole = 1÷(hole/min)
= 1÷0.058hole/min
= 17.24min/hole
b) 17.1
but TWO shovels in the same hole simultaneously is difficult.
Let the depth of the hole = x together they dig x/30 + x/40 = T Divide x by T you get the answer. 6th class problem
Nice job
17.1
The answer is D 35mins
Stupid multiple choice again, so we probably can eliminate some of the answers. It is quite easy to understand that if you take an average working time of 35 minutes the job together will take around 35/2 = 17 minutes. So answer C and D can be eliminated and answer B as the most likely result.
Now let's calculate the working speed (V):
V ted = 1 job / 30 min
V ed = 1 job / 40 min
V together = (1/30 + 1/40) = 4/120 + 3/120 = 7/120 job/min so the time working together for 1 job
T together = 1 job / V together = 1 / (7/120) = 120/7 = 17 1/7 minutes so answer B.
Nice !
Ted digs 3,33% of the hole per minute, Ed digs 2,5% of the hole per minute. Together they dig 5,833% of the hole per minute. Divide 100% by 5,833%/min. and you get the answer.
with you getting LCD as 120. Then, I didnt follow?
Why not use 10 as the common denominator?
Got it correct
Very interesting thank you
Thanks for getting me up
All day cos they talk ,look at the tools ,complain that they need sharpening hand them to the foreman and say they refuse to use them till they're sharpened.
This is truly a management dumb question, they both don't fit the hole at the same time
They can fit if they are Leprechauns.
b) 17.1 min
29.6
The hole has to be bigger to fit both workers... also we don't know if they are actually team players or not... what if they only had one shovel... who's doing the delegating... this math doesn't make sense
Ted and Ed were being paid by the hour and the kept talking about their date last night. That's why it took 49 minutes. I came up with 17.5 minutes and then went with 17.1 since that was the closet to my answer.
35
But you know what is wrong about those answers, Both of them Cannot work at the same time in that hole... And Therefore the true answer is unattainable unless you just put a stopwatch on the Job as it is done... The job will be faster than one or the other working by themselves... But it will not 1/2 the time of the job...
I have a PhD in math. I've coached students on standardized tests at a number of levels. This is a terrible question. I hope it has never actually appeared on an exam. I knew the answer immediately because the "immediate and obvious" 35 was not obscured by the other 3 (exam coaching 101 - if an answer looks obvious, don't trust it, especially if the other answers aren't trying to "hide" it). So must be digging simultaneously (not given in the question) -- answer is between 15 and 20 minutes ( and answer (c) was strangely yet ridiculously close to given 30 minutes). So immediately focus on (a) and (b) (exam coaching 102 - should be able to quickly eliminate all but two answers). Answer (a) is practically half the 30 minutes, so can't possibly incorporate slower digger. Thus answer is (b). A well-coached student (i.e., from a well-off family) gets the correct answer with no knowledge of underlying mathematics whatsoever (exam coaching 103 - be number savvy). For those who can't afford elaborate coaching, the question is misleading -- two people digging the same hole at the same time? In under 30 minutes? Must be a shallow yet wide hole, else no room for two shovels in same hole. Completely reasonable for those without exam coaching to think that Ted dug first half of hole and Ed dug the second half -- only thing that "jives" with their mental image of a hole slightly wider than the shovel that digs it. Great!! Hard working kids from blue collar and under-represented groups get it wrong because they actually are around those that dig holes and would never assume hole independence of diggers as the question demands. Yes, it angers me to see these types of questions -- so reminiscent of the Soviet's "coffin problems" that were used to insure that Jews didn't get accepted into their Universities. Yes, these are the types of questions used to insure the "right" people pass and all others are destined to a lifetime of digging holes or the equivalent!
You’re so smart. You should start your own channel. If this studio channel can get 580+ subscribers you will surely get millions, because you’re so smart. Pat yourself on the back and admire yourself in the mirror.
If both were 30 it would be 15min. If both were 40 it would be 20min. Hint so greater than 15 but less than 20...17.1 seems right not 15.3
WOW! Talk about excess verbiage!! Assuming that each of holes are of a common volume, the the holes that each dug, would total up to the volume of one hole. So they could be working simultaneously but on different sites and not interferring with each other. Or they could coordinate their digs so they don't interfere. And there was nothing that said the holes are round, so they could work side by side. If he had said, there is a pool full of water and pump "A" takes 30 minutes to empty it and pump "B" takes 40 minutes, how long would it take if you used both pumps simultaneously. No shovel conflicts!!
It's 40+30÷2=35
35 minutes together.
Sorry, it will take 17.1 minutes.
120/7, slightly more than 17 minutes
On the other hand, if it is someone I know then it will take30 minutes and then after the break, 20 more to work off the 2 beers each has consumed.
Get real. Once beer is involved you must compute with imaginary numbers!
15 but for 10 for sure
Can't believe you spent 16 minutes to solve a problem by turning it into a formula without explaining how you arrived at that formula from first principles. A lot of woolly chatter and no actual learning. Just showing something parrot fashion. WHY is it 1/ted+1/ed? There are simpler quicker ways to do this that make logical sense. 1/minutes... That seems plucked out of the air. Tell folks where it counts from please.
It's D
Together that did it quicker than your very long winded explanation. Gezzz...stop with the upfront lecture about which choice is incorrect and get on with the actual problem.
17.1 min
That Ed is one lazy bastard. When you find yourself in a hole the first thing to do is stop digging.
35 minutes
B is my answer
Depends on how deep the hole is supposed to be.
30 min +40 min = 70min ÷2people =35 min
D
B
lots of assumptions that do not fit real life cooperative actions
What if they only dug half a Hole😊😊😊
1/2 + 1/2 = 1 whole hole. Job completed. Your welcome.
I will subscribe when you cut your videos down to one third the time. So frustrating
Juan and ten cousins can dig the hole much faster And cheaper!
I find you take a very long time to get to the point.
Why don't women ever dig holes?
Narrator beats around rhe bush too much in attempt to get subscribers. Work the problem quickly and why it's worked that way. Math is for KEEP IT SHORT and SIMPLE!
It is not about math, it’s about logistic and sociology
b)17.1
35
B
35