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
Working together at their respective rates
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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.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Another approach is to assign a nice value to the job.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
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
Answer: E
Cheers,
Brent
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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: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
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.
Answer: E
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Thanks a lot!Scott@TargetTestPrep wrote: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: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
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.
Answer: E
GMAT/MBA Expert
- Brent@GMATPrepNow
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Another approach is to assign a nice value to the job.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
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
Answer: E
Cheers,
Brent