# Indian in a canoe

CalJust
Posers and Puzzles 11 Oct '06 12:13
1. CalJust
It is what it is
11 Oct '06 12:13
Also an old one, but still good.

An indian is paddling his canoe upstream. (Make it a boy scout if you want to be PC).

At some point, his spare paddle falls into the water and drifts downstream without him noticing.

When he DOES notice tha he must have dropped it overboard, he turns his canoe around (instantaneously, of course, as in all puzzles) and now paddles downstream at the same relative speed to the stream as before.

After 20 minutes, he catches up with his paddle.

An observer on the bank noticed that during that time, the paddle had moved exactly one kilometer from the place where it was dropped.

What is the speed of the stream?

(See if you can figure out a simple, intuitive way without complicated Algebra)
2. 11 Oct '06 13:20
well if after20mins the distance travelled was 1km, in an hour it would be 3km so = 3km per hour. is that what you wanted the answer to be?
3. CalJust
It is what it is
11 Oct '06 14:45
Originally posted by mazziewag
well if after20mins the distance travelled was 1km, in an hour it would be 3km so = 3km per hour. is that what you wanted the answer to be?
The Indian travelled for 20 minutes downstream to catch up, after having gone an unspecified distance further upstream after having dropped it.
The paddle travelled for 1 km.

Can you explain your reasoning why you can just say 20 min equals 1 km??
4. 11 Oct '06 15:52
Originally posted by CalJust
Also an old one, but still good.

An indian is paddling his canoe upstream. (Make it a boy scout if you want to be PC).

At some point, his spare paddle falls into the water and drifts downstream without him noticing.

When he DOES notice tha he must have dropped it overboard, he turns his canoe around (instantaneously, of course, as in all puzzles) a ...[text shortened]... f the stream?

(See if you can figure out a simple, intuitive way without complicated Algebra)
First off you said that "he must have dropped it overboard" when it obviously "fell overboard without him noticing". did you mean to say "it must have dropped overboard"?

also how long was it before he noticed that the paddle was gone?

because it was 1km from where it was dropped not from where he [b]noticed it was dropped[b]. so you would add the time from when it was dropped to the time when he noticed it was dropped.

Give us that time. then it will be solvable.
5. 11 Oct '06 17:13
That joke's not funny at all.
6. CalJust
It is what it is
12 Oct '06 11:051 edit
Originally posted by liteswordatlitespeed
First off you said that "he must have dropped it overboard" when it obviously "fell overboard without him noticing". did you mean to say "it must have dropped overboard"?

also how long was it before he noticed that the paddle was gone?

because it was 1km from where it was dropped not from where he noticed it was dropped.
Give us that time. then it will be solvable.[/b]
First of all, darvlay, it's not supposed to be a joke!

Secondly, litesword, if you read the original again, it is quite clear.

The guy is moving upstream and his paddle falls overboard without him noticing. After going merrily onward an unspecified distance and time (could be and hour, could be ten minutes) he suddenly notices that his paddle is missing. At that point he turns around, and paddles swiftly downstream. After 20 minutes he reaches his paddle - that's all you know. The other bit of information (which must come from an independent observer, since obviously the canoeist did not mark the exact point where the paddle fell overboard) is that the paddle itself travelled only one kilometer.

From this information you should be able to figure out the speed of the river.
7. PBE6
Bananarama
12 Oct '06 14:371 edit
Originally posted by CalJust
Also an old one, but still good.

An indian is paddling his canoe upstream. (Make it a boy scout if you want to be PC).

At some point, his spare paddle falls into the water and drifts downstream without him noticing.

When he DOES notice tha he must have dropped it overboard, he turns his canoe around (instantaneously, of course, as in all puzzles) a ...[text shortened]... f the stream?

(See if you can figure out a simple, intuitive way without complicated Algebra)
Not sure about an intuitive solution, but the answer comes out of the equations:

vR = velocity of the river
vC = velocity of the canoe w.r.t. water surface
t1 = time it takes for Indian to realize he dropped the paddle
t2 = the time the Indian meets up with his paddle again

1. Position of paddle = (t, -vR*t)

2. Position of canoe = for tt1 (t, [vC-vR]*t1 - [vC+vR]*[t - t1])

3. [t2 - t1] = 20 min = 1/3 hr

4. vR*t2 = 1 km (paddle travels 1 km total)

There are 4 unknowns and 4 equations, so we can solve this system. I'll spare everyone the algebra, but if you let t = t2, and combine equations 1, 2 and 3 you get t1 = 1/3 and t2 = 2/3. Subbing the value for t2 into equation 4 you get vR = -1.5 km/hr, the negative sign indicating that the river runs backwards w.r.t. the observer on the bank.
8. 12 Oct '06 15:31
darnit! Too advanced! I'm only in precalculus!

9. Agerg
The 'edit'or
12 Oct '06 16:205 edits
hmm...I didn't bother to get my pencil and paper out, but if we think about it, so long as the boat's relative speed is the same before and after he notices the lost paddle then in reality the stream can for now be considered stationary (because if the boat just stops, the distance between boat and paddle remains constant)... from this we can deduce that it must have taken him 20 minutes to spot that he'd lost the paddle such that he could travel back at the same speed to collect his paddle in a further 20 mins
so in 40 mins the paddle moves 1 km...in 60 mins it travels 1.5km
10. PBE6
Bananarama
12 Oct '06 17:00
Originally posted by Agerg
hmm...I didn't bother to get my pencil and paper out, but if we think about it, so long as the boat's relative speed is the same before and after he notices the lost paddle then in reality the stream can for now be considered stationary (because if the boat just stops, the distance between boat and paddle remains constant)... from this we can deduce that it mu ...[text shortened]... addle in a further 20 mins
so in 40 mins the paddle moves 1 km...in 60 mins it travels 1.5km
Clever! I like it.
11. uzless
The So Fist
12 Oct '06 18:162 edits
Originally posted by Agerg
hmm...I didn't bother to get my pencil and paper out, but if we think about it, so long as the boat's relative speed is the same before and after he notices the lost paddle then in reality the stream can for now be considered stationary (because if the boat just stops, the distance between boat and paddle remains constant)... from this we can deduce that it mu addle in a further 20 mins
so in 40 mins the paddle moves 1 km...in 60 mins it travels 1.5km
Correct. However there is another intuitive solution.

You could assume the river is not moving (not all rivers flow all the time). If you did this you would also know how long ago the paddle miraculously jumped out of the canoe.

Since it took him 20 minutes to travel back to the paddle, it would have fallen out 20 minutes prior to him realizing.

The river speed is therefore 0km/hour AND he lost the paddle for a total of 40 minutes.
12. 12 Oct '06 20:50
Originally posted by uzless
Correct. However there is another intuitive solution.

You could assume the river is not moving (not all rivers flow all the time). If you did this you would also know how long ago the paddle miraculously jumped out of the canoe.

Since it took him 20 minutes to travel back to the paddle, it would have fallen out 20 minutes prior to him realizing.

The river speed is therefore 0km/hour AND he lost the paddle for a total of 40 minutes.
You cannot assume the river is not moving, because it was given that the paddle moved 1 km. I'm not sure how the paddle would move 1 km if the river were not flowing.
13. CalJust
It is what it is
16 Oct '06 06:06
Agerg and uzless are both correct. Congrats!

If you cannot imagine a stationary not-flowing river, imagine the indian simply walking along a moving conveyor belt.

He drops his paddle, after 20 minutes further walking he turns around, walks back and picks it up from where he dropped it.

The paddle moved 1 km in 2 x 20 minutes = 1,5 km/hr
14. 02 Nov '06 17:34
Maybe I'm dense, but I still don't understand how the paddle moves 1 km if the river is not flowing. What propelled the paddle if not the flow of the river?
15. uzless
The So Fist
02 Nov '06 20:23
Originally posted by UncleRobb
Maybe I'm dense, but I still don't understand how the paddle moves 1 km if the river is not flowing. What propelled the paddle if not the flow of the river?
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