Paul has 3 large identical empty open-top containers (C1, C2, C3) outside.
- He walks outside and soon after, at time 0 hours, a steady rain begins. Rain enters the containers at R gallons per minute (gpm).
- 7 minutes later, Paul starts emptying out C1 at a rate of J gpm. Exactly when C1 is empty, Paul starts emptying C2 out and finishes 42 minutes later.
- Exactly when he's done emptying out C2, it starts raining twice as hard (2R gpm) and Paul starts emptying out C3 twice as fast (at 2J gpm).
-When Paul finishes emptying C3, the rain stops.
1) At what time did Paul start emptying C3?
2) At what time did it stop raining?
If x is the length of time to empty C1 and y the time to empty C3, then
7R + x(R-J) = 0
(7+x)R + 42(R-J) = 0
(49+x)R + y(2R-2J) = 0
Excel solver gives x = 14 and y = 63. Also, incidentally, R can be any value so long as J = 1.5 * R.
1) Paul starts emptying C3 at t = 7 + x + 42 = 63 minutes.
2) It stopped raining 63 minutes later, at t = 126 minutes.
Posted by Charlie
on 2008-11-05 22:08:31