Problema Solution
Jonathon and Samantha row their canoe 28 miles downstream in 2 hours. After a picnic, they row back upstream. After 3 hours they only travel 12 miles. Assuming that they canoe at a constant rate and the river's current is constant, find the speed at which Jonathon and Samantha can row in still water.
Answer provided by our tutors
Let
v = the speed at which Jonathon and Samantha can row in still water
c = river's current
d1 = 28 mi the distance traveled downstream
t1 = 2 hr the time of the downstream trip
d2 = 12 mi the distance traveled upstream
t2 = 3 hr the time of the upstream trip
We will use speed = distance/time formula.
When traveling downstream:
v + c = d1/t1
v + c = 28/2
v + c = 14
When traveling upstream:
v - c = d2/t2
v - c = 12/3
v - c = 4
We have the following system of equations:
v + c = 14
v - c = 4
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click here to see the system of equations solved for v and c
........
v = 9 mph
c = 5 mph
The speed at which Jonathon and Samantha row in still water is 9 mph.