Question

A man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream. Find the speed of the current if the speed of the boat is 11 mph in still water?

Answer 1

The speed of the current is 40.34 mph approximately.

SOLUTION:

Given, a man can drive a motorboat 70 miles down the Colorado River in the same amount of time that he can drive 40 miles upstream.  

We have to find the speed of the current if the speed of the boat is 11 mph in still water. Now, let the speed of river be a mph.  Then, speed of boat in upstream will be a-11 mph and speed in downstream will be a+11 mph.

And, we know that, $\text{ distance } =\text{ speed }\times \text{ time }$

$\begin{array}{l}{\text { So, for upstream } \rightarrow 40=(a-11) \times \text { time taken } \rightarrow \text { time taken }=\frac{40}{a-11}} \\\\ {\text { And for downstream } \rightarrow 70=(a+11) \times \text { time taken } \rightarrow \text { time taken }=\frac{70}{a+11}}\end{array}$

We are given that, time taken for both are same. So $\frac{40}{a-11}=\frac{70}{a+11}$

$\begin{array}{l}{\rightarrow 40(a+11)=70(a-11)} \\\\ {\rightarrow 40 a+440=70 a-770} \\\\ {\rightarrow 70 a-40 a=770+440} \\\\ {\rightarrow 30 a=1210} \\\\ {\rightarrow a=40.33}\end{array}$