Question 499218
When the pool is full, we can say that 100% of the work has been done.
100% is simply 1.
.
One hose can fill the pool in 7 hours, so it does 1/7 of the job per hr.
.
The second host can fill the pool in 4 hr, so it does 1/4 of the job per hr.
.
How many hours does it take to fill the pool?
.
x = the hrs to fill the pool
.
(1/7 + 1/4)*x = 1
.
That says when we add the work done by the two hoses working together, and multiply by the time, we end up with 1 full pool.
1/7 + 1/4 = 4/28 + 7/28 = 11/28
.
11/28*x = 1
.
Multiply both sides by 28/11.
.
x = 28/11 hr
.
x = 2 6/11 hr
That works out to about 2 hr 33 minutes.
.
Checking the answer:
1/7*28/11 = 28/77 = 4/11
.
1/4*28/11 = 28/44 = 7/11
,
4/11 + 7/11 = 11/11 = 1
.
Answer:
It will take 28/11 = 2 6/11 hours to fill the pool.
.
Done.