SOLUTION: Two pumps can drain a pool in 36 hours. The older pump alone takes 30 hours longer to drain the pool than the newer one does alone. How long does the newer pump take to drain the p

Question 670533: Two pumps can drain a pool in 36 hours. The older pump alone takes 30 hours longer to drain the pool than the newer one does alone. How long does the newer pump take to drain the pool?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
New pump x hours
Old pump x+ 30 hours
New pump 1/x of the job in hour
Old pump 1/(x+ 30 )of the job in 1 hour
Together they take 1/x+ 1/(x+30 )of the job in 1 hour

Together they do 1/36 of the job in 1 hour
1/x + 1/(x+30 )= 1/ 36
LCD =x(x+30)
(x+30)+x=1/36(x+30)x
( 2x+30 ) *36 = x^2+ 30 x
72 x+ 1080 = x^2+ 30 x
x^2 -42 x -1080 = 0
Find the roots of the equation by quadratic formula

a= 1 b= -42 c= -1080

b^2-4ac= 1764 - -4320
b^2-4ac= 6084 = 78

)/
x1=( 42 + 78 )/ 2
x1= 60
x2=( 42 - 78 )/ 2
x2= -18
Ignore negative value
x = 60 hours Time taken by new pump
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