Question

Two students are canoeing on a river. While heading upstream, they accidentally drop an empty bottle overboard. They then continue paddling for 1.3 h, reaching a point 3.0 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) 5.3 km downstream from the turn-around point.

A.Assuming a constant paddling effort throughout, how fast is the river flowing?

B.

What would the canoe speed in a still lake be for the same paddling effort?

Express your answer in kilometers per hour.

Answer 1

A) Let is consider speed of boat in still water be s

Speed of current be c

Then speed of canoe in+ up stream (against stream) = s-c = Distance traveled /time taken

s-c = 3/15= 2.3 Km /h

s= 2.3 +c.......... eq (A)

Speed of canoe along down stream or along stream = s+c

Time take by the canoe to catch up with the bottle = 1.3+(distance travelel along down stream / speed along down stream)

Time taken = 1.3 + ( 5.3/s+c)......eq B

Time taken by the bottle = distnace it traveld / speed of strem = 5.3-3/c= 2.3/c........eq C

Both times must be equal hence eq B = eq C

1.3+(5.3/s+c) = 2.3/c

Adding eq 1 and 2 we get

2s = 2.3+5.3/t

Here c= 0.9 K/h

Or c= -2.3k/h

Taking positive value

c= 0.9 k/h

Which is speed of Stream.

B) From eq A

s= 2.3+c =2.3+0.9 = 3.2 k/h

Hence speed of Canoe in still water =3.2 k/h