SOLUTION: A 5 horsepower pump can empty a pool in 5 hours. A smaller 2 horsepower pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hour

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Question 5399: A 5 horsepower pump can empty a pool in 5 hours. A smaller 2 horsepower pump empties the same pool in 8 hours. The pumps are used together to begin emptying this pool. After 2 hours the 2 horsepower pump breaks down. How long will it take the 5 horsepower pump to empty the pool?
Answer by Abbey(339) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break this down by work:
Let 1%2F5 = the work that the 5 hp pump does each hour (If it can do the whole job in 5 hours, it is doing 1%2F5 of the job each hour
Let 1%2F8 = the work that the 2 hp pump does each hour.
Working together they do
%281%2F5%29%2B%281%2F8%29=%288%2F40%29%2B%285%2F40%29 or 13%2F40 of the job each hour
So in 2 hours, they have completed 2%2A%2813%2F40%29+or+%2813%2F20%29
This means that there is only 7%2F20 of the job left to do.
we know that the rate of work * time = amount of work completed
so: %281%2F5%29%2Atime=%287%2F20%29
multiply both sides by 5:
time+=+%287%2F4%29 or 1 and 3/4 hours.