Work & time problem

Question

Please help me with the following problem. My answer was 32/7. The correct answer seems to be 4. Please help explain.

Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?

A. 4 minutes

B. 32/7 minutes

C. 192/7 minutes

D. 224/7 minutes

E. 28 minutes

spartacus1412 · Answer

time taken would be 1/32 + 6/32 therefor, time taken should be 32/7 may I know the source of this question.

GMATGuruNY · Answer

cypherskull wrote:Please help me with the following problem. My answer was 32/7. The correct answer seems to be 4. Please help explain.

Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?

A. 4 minutes

B. 32/7 minutes

C. 192/7 minutes

D. 224/7 minutes

E. 28 minutes

6 times as fast as A = 6(A's rate).
6 times FASTER than A = (A's rate) + 6(A's rate) = 7(A's rate).

Let the tank = 32 units.
Rate for pipe A = w/t = 32/32 = 1 unit per minute.
Rate for pipe B = 7*1 = 7 units per minute.
Combined rate for A+B = 1+7 = 8 units per minute.
Time for A+B to fill the tank = w/r = 32/8 = 4 minutes.

The correct answer is A.

bhopalkararpit · Answer

Hello Sir,
if we solve in this way :-
Let tank's capacity be = 1 unit
time taken to fill by pipe A = 32 mins
Rate of pipe A = 1/32
rate of b is 6 times that of A, so -> rate of B = 6*1/32
now combined rate 1/32+6/32 multiplied by t = 1 (capacity)
> t = 32/7 ans
whats wrong in this, please explain

Regards

cypherskull · Answer

Hi,

Thanks for the explanation GuruNY. I think you hv pointed out a very crucial aspect of the gmat and that is "wording of a problem".

@bhopalkarapit - Quoting from GuruNY,

6 times as fast as A = 6(A's rate).
6 times FASTER than A = (A's rate) + 6(A's rate) = 7(A's rate).

This is where I went wrong too.

Scott@TargetTestPrep · Answer

cypherskull wrote:
Pipe A can fill a tank in 32 minutes. Pipe B can fill the same tank 6 times faster than pipe A. If both the pipes are connected to the tank so that they fill the tank simultaneously, how long will it take for the empty tank to overflow?

A. 4 minutes

B. 32/7 minutes

C. 192/7 minutes

D. 224/7 minutes

E. 28 minutes

We are given that pipe A can fill a tank in 32 minutes and pipe B can fill the same tank 6 times faster than pipe A. That means pipe B can fill the tank 7 times as fast as pipe A.

Thus, the rate of pipe A is 1/32 and the rate of pipe B is 7/32. We can let t = the number of minutes the pipes work together and create the following equation to determine t:

work of pipe A + work of pipe B = 1

(1/32)t + (7/32)t = 1

8t/32 = 1

t/4 = 1

t = 4

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

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