math word problem

Question

Two pipes can fill a tank in 62 minutes if both are turned on. If only one is used, it would take 23 minutes longer for the smaller pipe to fill the tank than the larger pipe. How long will it take for the smaller pipe to fill the tank?

Answer 1

1/x+1/(x+23) = 1/62

62x +62(23) + 62x = x^2 + 23x

x^2 -101x - 1426=0

use the quadratic formula

x = 101/2 +/-(1/2)sqr(101^2 +4(1426))

= about 63.06 + 50.5 = 113.56 minutes for the slower pipe alone

136.56 minutes for the faster pipe alone