Question

A motorboat takes 5 hours to travel 200 kilometers going upstream. The return trip takes 4 hours going downstream. Whatand what is the rate of the current?

Answer 1

Given:

A motorboat takes 5 hours to travel 200 kilometers going upstream.

Let the speed of the motorboat = x

And the rate of the current = y

Note: rate = distance over the time

so,

$\begin{gathered} x-y=\frac{200}{5} \\ x-y=40\rightarrow(1) \end{gathered}$

And The return trip takes 4 hours going downstream

So,

$\begin{gathered} x+y=\frac{200}{4} \\ x+y=50\rightarrow(1) \end{gathered}$

Solve the equations (1) and (2) to find x and y

Add the equations to eliminate y

$\begin{gathered} 2x=40+50 \\ 2x=90 \\ x=\frac{90}{2}=45 \end{gathered}$

Substitute into equation (2) to find y

$\begin{gathered} 45+y=50 \\ y=50-45 \\ y=5 \end{gathered}$

So, the answer will be:

Rate of the boat = 45 km/h

Rate of the current = 5 km/h