Question

A motorboat can go 8 miles downstream on a river in 20 minutes. It takes 30 minutes for the boat to go upstream the same 8 miles. Find the speed of the current

Answer 1

The speed of the current is 4 miles/hour

Explanation:

Let us assume that,

x = speed of the boat,

y = speed of the current.

We know that,

`\text{Speed}=\frac{\text{Distance}}{\text{Time}}`

A motorboat can go 8 miles downstream on a river in 20 minutes or
`(20)/(60)` hours.

`\Rightarrow x+y=(8)/((20)/(60))=(8* 60)/(20)`

`\Rightarrow x+y=24` --------------------------1

It takes 30 minutes for the boat to go upstream the same 8 miles.

`\Rightarrow x-y=(8)/((30)/(60))=(8* 60)/(30)`

`\Rightarrow x-y=16` ----------------------------2

Subtracting equation 1 and 2,

`\Rightarrow x+y-x+y=24-16`

`\Rightarrow 2y=8`

`\Rightarrow y=4` miles/hour