Question

A motorboat takes five hours to travel two hundred miles going upstream. The return trip takes four hours going down stream. What is the rate of the boat in Stillwater and what is the rate of the current?

Answer 1

Answer: $45\ mph$,  $5\ mph$

Step-by-step explanation:

Given

A motorboat takes 5 hours to travel 200 miles upstream and 4 hours to go downstream

Suppose the speed of motorboat in still water and rate of current be x and y respectively.

during upstream

$\Rightarrow 5=\dfrac{200}{x-y}\\\\\Rightarrow x-y=40\quad \ldots(i)$

During downstream

$\Rightarrow 4=\dfrac{200}{x+y}\\\\\Rightarrow x+y=50\quad \ldots(ii)$

Add (i) and (ii) we get

$\Rightarrow 2x=90\\\Rightarrow x=45\ mph$

$\therefore y=5\ mph$

Thus, the speed of boat in still water is $45\ mph$ and rate of current is $5\ mph$