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

Answer:

8 kilometer per hour

Step-by-step 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 $8\text{kmph}$