Question

A small motorboat travels 16 mph in still water. It takes hour longer to travel 74 miles going upstream than it does going downstreamFind the rate of the current (Hint: 16 + x = rate going downstream and 16 - x = rate going upstreamRound your answer to the nearest tenth)

Answer 1

To find:

The rate of the current.

Solution:

Given that the speed of boat in still water is 16 mph.

From the question, we have that it takes 1 hour longer to travel 74 miles going upstream than going downstream. So,

`\begin{gathered} (74)/(16-x)-(74)/(16+x)=1 \\ (74(16+x)-74(16-x))/(16^2-x^2)=1 \\ 1184+74x-1184+74x=256-x^2 \\ 148x=256-x^2 \\ x^2+148x-256=0 \end{gathered}`

On solving, the above quadratic equation, we get x = 1.70997.

Thus, the rate of current is 1.70997.