Question

Burt and ned paddle their canoe 10 miles upstream and 5 miles downstream in 7 hours. if they can paddle 4 mph in calm water, how fast is the current?

Answer 1

The current flow is 2.4mph.

To find the answer, we have to know about the streamline flow.

How to find the rate of flow of current?

The boat's speed will reduce by V miles per hour if it is moving upstream because the current, which moves at a speed of V miles per hour, will be pressing against it. The boat moves downstream at a pace of Vp-V miles per hour as a result. However, if the boat is moving downstream, the current will be pushing it faster, increasing the boat's speed by V miles per hour. The boat's downstream speed as a result is Vp+V miles per hour.

where; Vp is the paddling speed in calm water.

• It is given that, upstream distance is 10 miles, and downstream is 5 miles in 7 hours.
• Thus, the time taken for downstream is,

                     $t_d=\frac{S_d}{v_d}=\frac{5}{4+V}$  , where; S is distance and v is speed.

• Similarly, the time taken for upstream is,

                           $t_u=\frac{S_u}{v_u}=\frac{10}{4-V}$

• The total time taken is,

                $t=7hours=t_d+t_u$                  

• From this, the velocity of current is,

                       $\frac{5}{4+V}+\frac{10}{4-V} =7\\\\V=2.4mph$

Thus, we can conclude that, the current flow is 2.4mph.

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