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The 3 containers (Posted on 2008-11-05) Difficulty: 2 of 5
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?

See The Solution Submitted by pcbouhid    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution solution | Comment 2 of 5 |

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
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