Question

If a boat has two oil skimmers, one skimmer takes 60hrs to fill the boat, the second takes 50hrs to fill the boat, but it takes 30hors to drain the boat, how long will it take to fill the boat if the drain is left open?

Answer 1

Let time taken be t hrs.
Rate of 1st = 1/60 boats/hr
Rate of 2nd = 1/50 boats/hr
Rate of draining = 1/30 boats/hr
So:
\[\frac{1}{t}=\frac{1}{60}+\frac{1}{50}-\frac{1}{30}\]
Solve for t (t = 300)