Working together at their respective rates, two hoses fill a pool in 2 hours. If one of the hoses, working alone, could

BTGmoderatorLU wrote: ↑

Sun Apr 23, 2023 3:09 pm

Source: Veritas Prep

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

The OA is E

One 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