Story problem

Question

A water tank is connected to two pipes. When both pipes are open they can fill a tank in 5 hours. The larger of the pipes can fill the tank three hours sooner than the smaller pipe can. How long will it take the smaller pipe working alone to fill the tank? Round to nearest tenth of an hour. 

Answer 1

let x=time in hours it takes the smaller pipe to fill the tank

let x-3=time in hours it takes the larger pipe to fill the tank

1/x=that part of the tank filled by the smaller pipe in 1 hour

1/(x-3)=that part of the tank filled by the larger pipe in 1 hour

working together...

(1/x)(5)+(1/[x-3])(5)=1(job finished, tank filled)

multiply both sides by (x)(x-3)

5(x-3)+5x=(x)(x-3)

5x-15+5x=x²-3x

10x-15=x²-3x

x²-13x+15=0

using the quadratic formula...

(13+√169-60)/2

(13+√109)/2

using (13+√109)/2=(13+10.44)/2

23.44/2=11.72

x=11.7 hours

x-3=8.7 hours

the smaller pipe working alone takes 11.7 hours