document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #689612 by Boreal(15235)\"\" \"About 
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the 10 horsepower pump empties the pool in x hours, the 6 hp pump in x+30 hours
\n" ); document.write( "in 1 hour, it empties 1/x of the pool, the 6 hp pump 1/(x+30) hours.
\n" ); document.write( "both pumps together take 36 hours, so in 1 hour they do 1/36 of the pool.\r
\n" ); document.write( "\n" ); document.write( "Therefore (1/x)+(1/(x+30)=1/36
\n" ); document.write( "multiply through by 36x(x+30)
\n" ); document.write( "36(x+30)+36x=x^2+30x
\n" ); document.write( "36x+1080+36x=x^2+30x
\n" ); document.write( "0=x^2-42x-1080
\n" ); document.write( "x=(1/2)(42+/- sqrt (1764+4320); sqrt term is 78
\n" ); document.write( "x=120/2=60, only positive root
\n" ); document.write( "(factors into (x-60)(x+18)
\n" ); document.write( "10 hp pump takes 60 hours. ANSWER
\n" ); document.write( "6 hp pump takes 96 hours
\n" ); document.write( "together
\n" ); document.write( "1/60+1/90=(90+60)/5400=150/5400=1/36
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