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.

Answer 2

Using the speed - distance relationship, the distance which should be paddled upstream in other to ensure total time taken is 2 hours should be 5.71 miles.

• Paddling speed = 7 mph
• Total paddling time = 2 hours
• Flow speed towards sea = 3 mph

Recall :

• Time taken = $\frac{distance}{speed}$

• Let distance = d

Upstream speed :

• Paddling speed - flow speed = 7mph - 3mph = 4 mph

• Upstream time = $\frac{d}{4}$

Downstream speed :

• Paddling speed + flow speed = 7mph + 3mph = 10 mph

• Downstream time = $\frac{d}{10}$

Total time taken :

Upstream time + downstream time

Total time = $\frac{d}{4} + \frac{d}{10} = 2$

$\frac{(10d + 4d)}{40} = 2$

$\frac{(14d)}{40} = 2$

Cross multiply :

$14d = 80$

Divide both sides by 14

$d = \frac{80}{14} = 5.71 \: miles$

Therefore, the distance paddled upstream should be 5.71 miles.

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