Problema Solution

A canoe travels on a river whose current is running at 6 miles per hour. After traveling 105 miles​ upstream, the canoe turns around and makes the 105 mile trip back downstream. The trip up and back takes 6

hours. What is the speed of the canoe in still​ water?

Answer provided by our tutors

Let

v = the speed of the canoe in still​ water, v>0

c = 6 mph the current of the river

d = 105 mi the distance traveled in each direction

t = 6 hr the time of the trip

The speed of the canoe when traveling upstream is: v - c = v - 6

The speed of the cane when traveling downstream is: v + c = v + 6

Since speed = distance/time follows time = distance/speed.

The time the upstream travel plus the time of the downstream travel equals t = 6 hours:

d/(v - c) + d/(v + c) = t

105/(v - 6) + 105/(v + 6) = 6

........

click here to see the equation solved for v

........

v = 36 mph

We need to ignore the negative solution -1 since the speed can not be negative.

The speed of the canoe in still water is 36 mph.