Question

In still water Derek can paddle his canoe at 6.5 km/h. On a river the canoe travels faster
downstream than upstream because of the current. In the morning Derek travels upstream
and takes 5 hours and then in the afternoon Derek travels downstream the same distance
and takes 2 hours. What is the speed of the current? Answer to the nearest tenth.

Answer 1

Explanation:

Let the speed of the current be x.

Given,

Derek paddles his canoe at a speed of 6.5 km/h in still water.

So,

His speed when going downstream = (6.5 + x) km/h

His speed when going upstream = (6.5 - x) km/h

It is also given that

Time taken to go downstream = 2 hours

Time taken to go upstream = 5 hours

Since distance upstream and downstream remains the same, we can say that

$\mathsf{(6.5+x)\times2=(6.5-x)\times5}$ [∵ $\mathsf{Distance = Speed\times Time}$]

$\mathsf{==>13+2x=32.5-5x}$

$\mathsf{==>2x+5x=32.5-13}$

$\mathsf{==>7x=19.5}$

∴ $\mathsf{x=\frac{19.5}{7}= 2.8\: km/h\:(approximately)}$

Hence, the speed of the current is 2.8 km/h

Answer: 2.8 km/h

I hope this helps. :D