| Title: | Mathematics at DEC |
| Moderator: | RUSURE::EDP |
| Created: | Mon Feb 03 1986 |
| Last Modified: | Fri Jun 06 1997 |
| Last Successful Update: | Fri Jun 06 1997 |
| Number of topics: | 2083 |
| Total number of notes: | 14613 |
Another puzzle without too many numbers in it, that may be solved in your head: A canoeist launches from a dock onto a river, and paddles ONE MILE upstream, at which point she drops her hat into the river. She continues paddling upstream for ANOTHER HOUR, and then returns to the dock. Having paddled at the same rate the whole time, she manages to reach the dock AT THE SAME TIME as the drifting hat. How fast is the river flowing ? /Eric
| T.R | Title | User | Personal Name | Date | Lines |
|---|---|---|---|---|---|
| 317.1 | TOROID::MCKINLEY | Tue Jul 16 1985 17:56 | 57 | ||
Solution follows <FF>
| Dx | Dy |
| | |
| | |
^dock ^hat dropped ^turnaround
<---F
<---P--->
Dx = Distance from dock to hat drop = 1 mile
Dy = Distance from hat drop to turnaround point
F = Flow rate of the river (to the left, downstream)
P = Paddling rate of the canoe (up or downstream)
Known:
Dx = 1 mile
Dy/(P-F) = 1 hour (time to turnaround)
Dy (Dy + Dx) Dx (time to turnaround, then back to dock =
-- + --------- = -- time for hat to drift to dock)
(P-F) (P + F) F
substitute 2 into 3:
(P - F) + 1 1
1 + ----------- = -
(P + F) F
mult by (P + F)
P + F
P + F + P - F + 1 = -----
F
Reduce, mult by F
2PF + F = P + F
2PF = P
2F = 1
F = 1/2 mile/hour
But I didn't do it in my head. What's the easy way?
---Phil
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| 317.2 | SPRITE::OSMAN | Thu Jul 18 1985 18:10 | 12 | ||
*** spoiler follows *** The easy way is to remember that the dropped hat and the canoeist are in the same frame of reference, so we needn't worry about river flow or dock position at all. Hence canoeist merely paddles away from hat for an hour and an hour back. Therefore hat has flowed down the river for two hours. We're given that during this two hour period, hat flows to dock, and that hat started flowing from a mile away . . . one mile of flow in two hours is 1/2 mph (you are right). /eric | |||||