Two pumps working together empty a pool in 24 minutes. Working separately, it takes the smaller pump 15 minutes longer than the larger pump. How long would it take each pump to empty the pool by i

Question

Two pumps working together empty a pool in 24 minutes. Working

separately, it takes the smaller pump 15 minutes longer than the larger

pump. How long would it take each pump to empty the pool by itself ?

Answer 1

1/x + 1/(x+15) = 1/24 multiply by 24x(x+15)

24(x+15) + 24x = x^2 + 15x

x^2 -33x - 360 = 0

x=33/2 + (1/2)sqr(33^2 + 1440) = about 83/2= 41.5 minutes

x+15 = 56.5 minutes

if they both worked at 48 minutes each, they'd complete it together in half that time= 24 minutes. add and subtract about 15/2 = 7.5

average of 41.5 and 56.5 is 98/2= 49 49/2 = close to 24