Function to model combined rate

Question

Pipe A takes 20 hours longer to fill swimming pool than pipe B. Together, pipe A and pipe B can fill the swimming pool in 30 hours.

How do I write a function that models the combined rate of the two pipes in relation to the time it takes for pipe B to do it by itself?

Answer 1

A=20+B

1/A + 1/B = 1/30

1/(20+B) + 1/B = 1/30

multiply by 30(B)(20+B) to get remove fractions

30B + 30(20+B) = B(20+B) = 20B + B^2

B^2 -40B =600

complete the square

B^2 -40B + 400 = 600+400

(B-20)^2 = 1000

B-20 = sqr1000 = 10sqr10 = about 33

B = 20 +33 = 53 hours

A = 53 + 20 = 73 hours

Answer 2

The formula to use is: 1/job 1 + 1/job 2 = 1/total

Let x = time to fill with Pipe B

x+20 = time to fill Pipe A

1/x + 1/(x+20) = 1/30 Solve for x and this will give you the rates of the individual pipes.