Question

A motorboat travels 408 kilometers in 6 hours going upstream and 882 kilometers in 9 hours going downstream. What is the rate of the boat, and what is the rate of the current?

Answer 1

We have the next variables

x = speed of the boat in still water

y = speed of the current

(x-y) = Upstream speed

(x+y) = downstream speed

So we have the next equations for the distance

`\begin{gathered} 6\mleft(x-y\mright)=408 \\ \end{gathered}`
`\begin{gathered} 9(x+y)=882 \\ \end{gathered}`

We simplify each equation

`\begin{gathered} x-y=68 \\ x+y=98 \end{gathered}`

we sum both equations

`\begin{gathered} 2x=166 \\ x=(166)/(2) \\ x=83 \end{gathered}`

Then we calculate the y

`\begin{gathered} y=98-x \\ y=15 \end{gathered}`

x = speed of the boat in still water=83 km/hr

y = speed of the current 15 km/hr