Answer:
8 kilometer per hour
Step-by-step explanation:
Given: Dani spend her summers at her grandparents cabin in canada. The cabin is [tex]42[/tex] kilometers upriver from the nearest town. The river has a downstream current of [tex]4[/tex] kilometers per hour.
To Find: If Dani can canoe from the cabin to town and back in [tex]14[/tex] hours, what is her average canoeing speed in still water.
Solution:
Let the speed of Dani in still water is [tex]=\text{s}[/tex]
speed of downstream current is [tex]=4\text{kmph}[/tex]
speed of Dani in downstream current [tex]=\text{s}+4[/tex]
speed of Dani in upstream current [tex]=\text{s}-4[/tex]
Now,
Total time taken by Dani to canoe from the cabin to town and back [tex]=14\text{hours}[/tex]
[tex]\frac{42}{\text{s}-4}+\frac{42}{\text{s}+4}=14[/tex]
[tex]{\text{s}}^2-6\text{s}-16=0[/tex]
[tex](\text{s}-8)(\text{s}+2)[/tex]
[tex]\text{s}=8,-2[/tex]
as speed can't be negative the average speed of dani in still water is [tex]8\text{kmph}[/tex]
