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Working together at their respective rates

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 1 member reply
BTGmoderatorDC Moderator
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Working together at their respective rates

Thu Sep 21, 2017 6:32 am
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours

How will i formulate a formula here? Need experts advice. Thanks

OAE

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Brent@GMATPrepNow GMAT Instructor
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Fri Sep 22, 2017 6:24 am
lheiannie07 wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
Another approach is to assign a nice value to the job.
In this case, we need a value that works well with the given information (2 hours and 3 hours).
So, let's say the job consists of filling a pool containing 6 liters of water

One of the hoses, working alone, takes 3 hours to fill the pool
We'll call this hose A.
Let A = the rate of work of this hose
If it takes 3 hours for this hose to fill a 6-liter pool, then....
A = 6/3 = 2 liters per hour (since rate = output/time)

Working together at their respective rates, two hoses fill a pool in 2 hours.
Let B = the rate of work of the other hose
So, the COMBINED rate = A+B
If it takes 2 hours for the combined hoses to fill a 6-liter pool then....
A+B = 6/2 = 3 liters per hour (since rate = output/time)

So, if A = 2 liters per hour, and A+B = 3 liters per hour
Then we can see that B = 1 liter per hour

How long would it take the other hose (hose B) to fill the pool alone?
Time = output/rate = 6/1 = 6 hours

Cheers,
Brent

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Scott@TargetTestPrep GMAT Instructor
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Mon Sep 25, 2017 3:33 pm
lheiannie07 wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
We can let n = the time, in hours, it takes the other hose to fill the pool alone. Thus, the rate of that hose = 1/n. Since the rate of the known hose = 1/3 and the combined rate = 1/2, we have:

1/n + 1/3 = 1/2

Multiplying by 6n, we have:

6 + 2n = 3n

6 = n

Thus, the other hose takes 6 hours to fill the pool.

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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Thu Sep 21, 2017 7:43 pm
Hi lheiannie07,

This question is a standard example of a Work Formula question (with 2 'entities' working on a job together). When this type of question has no 'quirks' to it (such as 3 or more entities or one of the entities stops working partway through the job), you can use the Work Formula to answer it:

Work = (A)(B)/(A+B) = amount of time to complete the job while working together (where A and B are the two individual times it takes to do the job).

In this prompt, we know that one of the hoses takes 3 hours to do the job alone and that the two hoses (working together) can complete the job in 2 hours....

(3)(B)/(3+B) = 2 hours
3B = (2)(3+B)
3B = 6 + 2B
B = 6 hours

Thus, it would take the second hose 6 hours to fill the pool by itself.

GMAT assassins aren't born, they're made,
Rich

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BTGmoderatorDC Moderator
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Wed Jan 10, 2018 12:15 am
Scott@TargetTestPrep wrote:
lheiannie07 wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
We can let n = the time, in hours, it takes the other hose to fill the pool alone. Thus, the rate of that hose = 1/n. Since the rate of the known hose = 1/3 and the combined rate = 1/2, we have:

1/n + 1/3 = 1/2

Multiplying by 6n, we have:

6 + 2n = 3n

6 = n

Thus, the other hose takes 6 hours to fill the pool.

Thanks a lot!

GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
11487 messages
Followed by:
1229 members
5254
GMAT Score:
770
Wed Jan 10, 2018 7:07 am
lheiannie07 wrote:
Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could fill the pool in 3 hours, how long would it take the other hose to fill the pool alone?

A. 2 hours
B. 3 hours
C. 4 hours
D. 5 hours
E. 6 hours
Another approach is to assign a nice value to the job.
In this case, we need a value that works well with the given information (2 hours and 3 hours).
So, let's say the job consists of filling a pool containing 6 liters of water

One of the hoses, working alone, takes 3 hours to fill the pool
We'll call this hose A.
Let A = the rate of work of this hose
If it takes 3 hours for this hose to fill a 6-liter pool, then....
A = 6/3 = 2 liters per hour (since rate = output/time)

Working together at their respective rates, two hoses fill a pool in 2 hours.
Let B = the rate of work of the other hose
So, the COMBINED rate = A+B
If it takes 2 hours for the combined hoses to fill a 6-liter pool then....
A+B = 6/2 = 3 liters per hour (since rate = output/time)

So, if A = 2 liters per hour, and A+B = 3 liters per hour
Then we can see that B = 1 liter per hour

How long would it take the other hose (hose B) to fill the pool alone?
Time = output/rate = 6/1 = 6 hours

Cheers,
Brent

_________________
Brent Hanneson â€“ Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

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