Question

Dani spend her summers at her grandparents cabin in canada. The cabin is 42 kilometers upriver from the nearest town. The river has a downstream current of 4 kilometers per hour. If Dani can canoe from the cabin to town and back in 14 hours, what is her average canoeing speed in still water?

Answer 1

8 kilometer per hour

Explanation:

Given: Dani spend her summers at her grandparents cabin in canada. The cabin is
`42` kilometers upriver from the nearest town. The river has a downstream current of
`4` kilometers per hour.

To Find: If Dani can canoe from the cabin to town and back in
`14` hours, what is her average canoeing speed in still water.

Solution:

Let the speed of Dani in still water is
`=\text{s}`

speed of downstream current is
`=4\text{kmph}`

speed of Dani in downstream current
`=\text{s}+4`

speed of Dani in upstream current
`=\text{s}-4`

Now,

Total time taken by Dani to canoe from the cabin to town and back
`=14\text{hours}`

`\frac{42}{\text{s}-4}+\frac{42}{\text{s}+4}=14`

`{\text{s}}^2-6\text{s}-16=0`

`(\text{s}-8)(\text{s}+2)`

`\text{s}=8,-2`

as speed can't be negative the average speed of dani in still water is
`8\text{kmph}`