Question 417447
A 5 hp pump can empty a pool in 5 hrs.
 A smaller, 2 hp pump empties the same pool in 8 hours.
 The pumps are used together to begin emptying this pool.
 After two hours, the 2 hp pump breaks down.
 How long will it take the larger pump to empty the pool?
:
Let t = time for the larger pump to complete emptying the pool
:
Operating time of the larger pump = (t+2)
Operating time of the smaller pump = 2
:
Let the completed job = 1; (an empty pool)
:
{{{((t+2))/5}}} + {{{2/8}}} = 1
multiply by 40
40*{{{((t+2))/5}}} + 40*{{{2/8}}} = 40(1)
cancel the denominators and you have:
8(t+2) + 5(2) = 40
:
8t + 16 + 10 = 40
8t + 26 = 40
8t = 40 - 26
8t = 14
t = 14/8
t = 1.75 hrs for the large pump to complete the job (Total time of large pump = 3.75)
:
:
Check this:
3.75/5 + 2/8 =
.75 + .25 = 1; confirms our solution