A motorboat takes five hours to travel two hundred miles going upstream. The return trip takes four hours going down stream. Wha

Question

2 years ago

13

t is the rate of the boat in Stillwater and what is the rate of the current?

1 answer:

Yuri [45] · Answer 1 · 2022-09-10T06:43:12+03:00

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 $5\ mph$