Find the speed the kayaker would make in still water?

Question

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.

(Hint: The distance is the same both upstream and downstream and can be represented by "d." The rate is tricky. The trip downstream (with the current) is faster than the upstream trip (against the current). We don't know the speed the kayaker makes in still water, so we can represent that with "r." We do know that going with the current will add 6mph to this rate (r + 6), and going against the current will subtract 6mph from his rate (r - 6). Now we can write two equations (we have two unknowns). Using d = rt again, the equation upstream is: d = (r - 6)3. You write the equation for the equation downstream, and solve the system. Don't forget the units in your answer.)

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Answer 1

A kayaker paddled 2 hours with a 6 mph current in a river. The return trip against the same current took 3 hours. Find the speed the kayaker would make in still water.

(Hint: The distance is the same both upstream and downstream and can be represented by "d." The rate is tricky. The trip downstream (with the current) is faster than the upstream trip (against the current). We don't know the speed the kayaker makes in still water, so we can represent that with "r." We do know that going with the current will add 6mph to this rate (r + 6), and going against the current will subtract 6mph from his rate (r - 6). Now we can write two equations (we have two unknowns). Using d = rt again, the equation upstream is: d = (r - 6)3. You write the equation for the equation downstream, and solve the system. Don't forget the units in your answer.)

Let r=rate of kayaker

with stream = r+6 took 2hours

against stream = r-6 took 3 hours

rate * time = distance

(r+6)*2 = (r-6)*3

2r +12 = 3r - 18

30 = r

30mph is the rate of the kayaker without the current