Ted can dig a hole in 30min, Ed can do it in 40min, how long will it take if they work together? 

As soon as they begin they have dug a hole

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.

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.

Wow he goes on and on!

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 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.

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.

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.

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.

Depends on when one gets out of the hole and lets the other in to dig for awhile.

"Before i go off on a tangent" Math pun !!!

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.

Hopefully the supervisor didn't get Ed and Ted's work mixed up for hourly pay.

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!

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?😂

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.

Is there a video that explains how you arrived at the formula that you used?

Very interesting thank you

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.

Nice job

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.

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)

Thanks for getting me up

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.

All holes being equal. And what about elbow space?

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.

b)17.1

Time total = T1xT2/T1+T2=17.14

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.

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

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?

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.

JC… I can’t even take the Mambi pamby voice.

The way you state the problem is ambiguous. The time you gave is If they take turns digging. Not if they work together.

Sir please give us prove of this formula 😢😢

Why not use 10 as the common denominator?

Got it correct

The answer is D 35mins

17.1

b) 17.1 min

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.

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.

Deu 17,1 min, letra B.

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

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 !

Product over the Sum as long as the units are the same

29.6

with you getting LCD as 120. Then, I didnt follow?

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.

17.1 min

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

I may have known what you ment but the question was terrible. Two people cannot dig a hole at the same time.

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...

35

It's 40+30÷2=35

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.

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

It's D

35 minutes together.

That Ed is one lazy bastard. When you find yourself in a hole the first thing to do is stop digging.

15 but for 10 for sure

B is my answer

Sorry, it will take 17.1 minutes.

35 minutes

B

D

Depends on how deep the hole is supposed to be.

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.

30 min +40 min = 70min ÷2people =35 min

lots of assumptions that do not fit real life cooperative actions

Juan and ten cousins can dig the hole much faster And cheaper!

I will subscribe when you cut your videos down to one third the time. So frustrating

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.

What if they only dug half a Hole😊😊😊

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