A kayak wint up a river and back in 6 hours If their rate up

A kayak wint up a river and back in 6 hours. If their rate up the river was 2 miles per hour and back 4 miles per hour, how far did they go up the river?

Solution

Let x be time taken upstream and y time taken downstream.
Total number of hours is: x + y = 6hrs
Given speed upstream is 2miles per hour and speed downstream is 4 miles per hour.
the distance traveled upstream = distance traveled downstream
==>speed upstream * time taken = speed downstream * time taken
2 *x = 4 * y
Substitute for y in the above
2 * x = 4 * (6-x)
2(x) = 24 - 4x
6x = 24
x = 24 /6
x = 4hrs

The time taken upstream is 4hrs
we know that..
distance traveled upstream = speed upstream * time taken
= 2 * 4 = 8 miles

Distance traveled upstream is 8 miles