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
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click here to see the equation solved for v
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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.