Question

Two taps together fill a tank in 9 3/8 hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

Answer 1

Answer:

1/x + 1/y = 1/75/8      (y=x-10)given

1/x + 1/x-10 =  8/75

$x-10+x/x^{2}-10x= 8/75$

$2x-10/x^{2}-10x=8/75$

$8 x^{2} -230x+750=0$

$2(4x^{2} -115x+375)=0$

$4x^{2} -100x-15x+375=0$

$4x(x-25)-15(x-25)=0$

$(4x-15) (x-25)$

x=15/4 , x=25