Question

A motorboat travels 280 kilometers in 5 hours going upstream and 936 kilometers in 9 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?

Answer 1

Let x = the speed of the boat in still water while y = the rate/speed of the current in km/h.

Recall that:

upstream speed = speed of the boat in still water - speed of the current.

`upstream\text{ }speed=x-y`

downstream speed = speed of the boat in still water + speed of the current.

`downstream\text{ }speed=x+y`

Let's calculate the upstream and the downstream speed of the motorboat based on the given distance and time traveled.

`upstreamspeed=(280km)/(5hrs)=(56km)/(h)`
`downstreamspeed=(936km)/(9hrs)=(104km)/(h)`

Hence, the upstream speed is 56 km/hour. The downstream speed is 104 km/h.

From the equation above, we can form the following equations:

`\begin{gathered} 56=x-y \\ 104=x+y \end{gathered}`

To solve for x and y, we can use the elimination method.

1. Eliminate the variable "y" by adding the two equations.

`(x-y)+(x+y)=56+104`
`2x=160`

2. Divide both sides by 2.

`(2x)/(2)=(160)/(2)`
`x=80`

The value of x is 80.

3. Let's solve for "y" by replacing "x" with 80 in any of the two equations above.

`104=x+y`
`104=80+y`
`\begin{gathered} 104-80=y \\ 24=y \end{gathered}`

The value of y is 24.

Answer:

The rate of the boat in still water is 80 km per hour. The rate of the current is 24 km per hour.