Question 1074939: A swimming pool can be emptied in 36 hours using a 10-horsepower pump along with a 6-horsepower pump. The 6-horsepower pump requires 30 hours more than the 10-horsepower pump to empty the pool when working by itself. How long would it take to empty the pool using just the 10-horsepower pump?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the 10 horsepower pump empties the pool in x hours, the 6 hp pump in x+30 hours
in 1 hour, it empties 1/x of the pool, the 6 hp pump 1/(x+30) hours.
both pumps together take 36 hours, so in 1 hour they do 1/36 of the pool.
Therefore (1/x)+(1/(x+30)=1/36
multiply through by 36x(x+30)
36(x+30)+36x=x^2+30x
36x+1080+36x=x^2+30x
0=x^2-42x-1080
x=(1/2)(42+/- sqrt (1764+4320); sqrt term is 78
x=120/2=60, only positive root
(factors into (x-60)(x+18)
10 hp pump takes 60 hours. ANSWER
6 hp pump takes 96 hours
together
1/60+1/90=(90+60)/5400=150/5400=1/36
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