Working together at their respective rates

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

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

Answer: E

Cheers,
Brent

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.

Answer: E

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

Answer: E

Cheers,
Brent