Two pipes that are open at the same time can

fill a pool in 12 hours. When only Pipe A is open, it
can fill the pool 7 hours longer than when only Pipe
B is open. Find how long Pipe A can fill the pool
when it is the only pipe open?

(1 / A) + (1 / B) = 1 / 12

(1 / A) + [1 / (A - 7)] = 1 / 12

12 A - 84 + 12 A = A * (A - 7)

24 A - 84 = A² - 7 A

0 = A² - 31 A + 84

factor the quadratic to find A