Rate of change math question

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 compute how long will it take for pipe A to fill the swimming pool by itself and how long will it take for pipe B to fill the swimming pool by itself? How do I determine the rate of change function for the rate of pipe A and pipe B together? For the function, how do I determine what would be its domain for filling the swimming pool?

Answer 1

Hi John H.,

This isn't a question of functions and rates of change of functions, it's a problem in purely algebra. Set up the respective hose rates as A and B, in pool/hr. Then A + B = 1/30 (together they fill in 30 hr) and 1/A - 1/B = 20 (it takes A 20 hr more to fill than it takes B) . Reckon you can solve that?

Anyone who insists on domains for filling swimming pools -- let's just say they've "gone off the deep end"?

--Cheers, --Mr. d.

Answer 2

Let x = number of hours for pipe B to fill the pool on its own

Then x + 20 = number of hours for pipe A to fill the pool by itself

1/x = portion of pool filled by pipe B in one hour

1/(x+20) = portion of pool filled by pipe A per hour

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

30(x+20) + 30x = x(x+20)

60x + 600 = x² + 20x

x² - 40x - 600 = 0

Now, solve for x.