Question

A river flows at a speed of 3 mph towards sea. A woman in a canoe can paddle through water at a speed of 7 mph. She wishes to paddle for a total time of 2 hours, first upstream (away from the sea) then turning round and paddling back to her starting point. How long should she paddle upstream?

Answer 1

Answer:

She can paddle 5.71 miles upstream.

Explanation:

A woman in a canoe can paddle through water at a speed of 7 mph

Speed with which women can paddle = 7 mph

A river flows at a speed of 3 mph towards sea.

Speed of river = 3 mph

She need to paddle for 2 hours.

Let the distance paddled to upstream be d.

We have

    Velocity to upstream = 7 - 3 = 4 mph

    Velocity to downstream = 7 + 3 = 10 mph  

    $\texttt{Time for upstream = }\frac{d}{4}\\\\\texttt{Time for downstream = }\frac{d}{10}$

We have

          $\frac{d}{4}+\frac{d}{10}=2\\\\10d+4d=2\times 4\times 10\\\\14d=80\\\\d=5.71miles$

She can paddle 5.71 miles upstream.