Difficult math word question

Question

Two pipes together can fill a large tank in 10 hr. One of the pipes, used alone, takes 15 hours longer than the other to fill the tank. How long would each pipe take to fill the tank alone? My question is how to define the slower pipe’s rate in terms of the other pipe. Would it be 1/15 or (x + 1/15) and why?

Answer 1

x=# of hours it takes the fast pipe alone

x+15=# of hours it takes the slow pipe alone

(1/x)=what part of the job is done in one hour by the fast pipe

(1/[x+15])=what part of the job is done in one hour by the slow pipe

(10)(1/x)+(10)(1/[x+15])=1  job done

multiply both sides by the LCM which is (x)(x+15)

10(x+15)+10(x)=x(x+15)

10x+150+10x=x^2+15x

20x+150=x^2+15x

x^2+15x-20x-150=0

x^2-5x-150=0

factor

(x-15)(x+10)=0

x-15=0

x=15 hours for the fast pipe

15+15=30 hours for the slow pipe

(10)(1/15)+(10)(1/30)=1

2/3 + 1/3=1

1=1