math question please help!!!

Question

Two drainpipes working together can drain a pool in 20 hours. Working​ alone, the smaller pipe would take 30 hours longer than the larger pipe to drain the pool. How long would it take the smaller pipe alone to drain the​ pool?

Answer 1

Let L = the # of hrs for the larger pipe to drain the pool, then L + 30 = the number of hours for the small pipe.

(1/L) + [1/{L + 30)] = 1/20

This equation gives the quadratic L² - 10L - 600 = 0

One of the roots is extraneous. You should derive the quadratic and solve it to get L = and S = 60

Now why the initial equation? The terms which look like reciprocals are RATES and if you use rate * time = work done, you will see that the time divides out and you are left with the equation I first wrote.