Work & time problem

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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

Work & time problem

by cypherskull » Wed May 02, 2012 1:50 pm

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

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Source: Beat The GMAT — Problem Solving | Wed May 02, 2012 1:50 pm

spartacus1412: Master | Next Rank: 500 Posts; Posts: 110; Joined: Wed Feb 22, 2012 11:28 pm; Location: India; Thanked: 13 times; Followed by:1 members

by spartacus1412 » Wed May 02, 2012 7:38 pm

time taken would be
1/32 + 6/32
therefor, time taken should be 32/7

may I know the source of this question.

Its do or die this time!
Practise, practise and practise.

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Wed May 02, 2012 7:55 pm

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.

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bhopalkararpit: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Fri Mar 02, 2012 10:50 am

by bhopalkararpit » Thu May 03, 2012 9:04 am

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

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cypherskull: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Sat Mar 31, 2012 3:39 am; Location: Calcutta; Thanked: 8 times

by cypherskull » Thu May 03, 2012 9:16 am

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.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Dec 13, 2017 1:06 pm

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

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