Quadratic Algebra Problem

Question

It takes the first pipe 9 more hours to fill the pool than the first and the second pipes together and 7 less hours than it would take the second pipe if it was working alone. How long would it take to fill up the pool if both pipes were working together?

Answer 1

the first pipe takes x hours alone to fill the pool

the second pipe takes y hours alone to fill the pool

working together the two pipes take z hours to fill the pool

(1/x)(z)+(1/y)z=(1/x)(z+9)

(1/x)(z-7)=(1/y)(z)

replace (1/y)(z) by (1/x)(z-7) in equation 1

(1/x)(z)+(1/x)(z-7)=(1/x)(z+9)

(z/x)+([z-7]/x)=([z+9]/x)

([z+z-7]/x)=([z+9]/x)

(2z-7)/x=(z+9)/x

since the denominators are equal, the numerators must be equal

2z-7=z+9

2z-z=9+7

z=16 hours to fill the pool if both pipes were working together