Problem Solving

I searched and didn't see this particular question answered yet, and I am simply stumped!

A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rate, to fill the empty tank if they began pumping at the same time?
Answers:
1/4
1/3
2/5
5/4
3/2

I just can't seem to get the equation in such a way that I end up with the GMATPrep correct answer. Help! Thanks very much.

MercedesMW wrote:I searched and didn't see this particular question answered yet, and I am simply stumped!

A small water pump would take 2 hours to fill an empty tank. A larger pump would take 1/2 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rate, to fill the empty tank if they began pumping at the same time?
Answers:
1/4
1/3
2/5
5/4
3/2

I just can't seem to get the equation in such a way that I end up with the GMATPrep correct answer. Help! Thanks very much.

small pump can fill 1/2 tank per hour
large pump can fill 2 tank per hour

If they work together they can fill (1/2 +2) = 5/2 tank per hour..

Lets assume that if they work together they need X hours to fill the tank. That means.

5/2 * X = 1

Solve for X to get 2/5

HTH,

Thank you! It was that last part I was missing - the 5/2 * X = 1. I stopped at 5/2. Thanks for your help!

We can also use the work formula to quickly solve this question.

Combined Time for a&b = (a*b)/(a+b)

where a and b are the individual times.

In this case a = 2 and b = 1/2, so:

(2 * 1/2) / (2 + 1/2) = 1/(5/2) = 2/5

You can also look for a pattern in these kind of questions.

The faster pump fills the tank in 1/2 hour. So the answer should be less than 1/2, making D & E wrong choices.

Now there are two pumps with different speeds, If the two pumps were having the same speed (equal to the speed of the faster pump), they would have taken half time. i.e. 1/4. But the second pump is slower, a lot slower, hence the answer cannot be (1/2)/2 = 1/4, making A as incorrect.

Now the tough part is eliminating between B & C. We know that faster pump is four times faster than slower pump, so the time taken should be reduced by 20% (80% faster & 20% slower). Thus the portion of water filled by faster pump needs to be only 80%. 80% of 1/2 is 2/5 and the right answer....

That's very helpful to be able to look at the problem from two different angles. I can tell I'm really rushing through the practice questions!

simplyjat wrote:You can also look for a pattern in these kind of questions.

The faster pump fills the tank in 1/2 hour. So the answer should be less than 1/2, making D & E wrong choices.

Now there are two pumps with different speeds, If the two pumps were having the same speed (equal to the speed of the faster pump), they would have taken half time. i.e. 1/4. But the second pump is slower, a lot slower, hence the answer cannot be (1/2)/2 = 1/4, making A as incorrect.

Now the tough part is eliminating between B & C. We know that faster pump is four times faster than slower pump, so the time taken should be reduced by 20% (80% faster & 20% slower). Thus the portion of water filled by faster pump needs to be only 80%. 80% of 1/2 is 2/5 and the right answer....

You are right. just to give you guys an example...

i took a Quant test on Sunday and i was running short of time in the end...

there was a question something like this
A types a doc in 2 hours
B types a doc in 4 hours
C types a doc in 5 hours

what is the ratio of time taken by A over time taken by B and C together...

this is how i solved it...

If C did it in 4 hours too, then B and C could do it together in 2 hours. But since C takes 5, they would type the doc in more than 2 hours. So the ratio would be 2 over something more than 2

hence the ratio would be less than 1

4 out of 5 choices had ratio more than 1...

I like the work formula that stuart brings up.
Its a great way to solve these and they gain you time to add to your next questions. a *b / a +b which yields the 2/5 answer

thanks for eveyone