Two students are canoeing on a river. While heading upstream, they accidentally

Question

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.5 h, reaching a point 2.2 km farther upstream. At this point they realize that the bottle is missing and, driven by ecological awareness, they turn around and head downstream. They catch up with and retrieve the bottle (which has been moving along with the current) 4.7 km downstream from the turn-around point. Assuming a constant paddling effort throughout, how fast is the river flowing? v_river = km/h What would the canoe speed in a still lake be for the same paddling effort? V_canoe = k/h

Explanation / Answer

Part A:

The students are paddling relative to the water, if they paddle in one direction for 1.5 hours then they must paddle in the other direction also for 1.5 hours to get back to the bit of water ( and the bottle ) that they started from.

Therefore, the distance that the water has moved in these (1.5 + 1.5) = 3.0 hours is given as (4.7 - 2.2)km
so the speed of the water is (4.7 - 2.2)km / 3.0 hrs = 0.83 km/hr

Part B:

Again, the students got 2.2 km upstream in the 1.5 hours

therefore, we have
(v- 0.83) * 1.5 = 2.2
=> v- 0.83 = 2.2 / 1.5 = 1.47

=> v = 1.47 + 0.83 = 2.3 km/hr
So, the canoe speed in still lake = 2.3 km/hr.

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