Rate of current

Question

A boat takes 8 hours to go 6 miles upstream and come back to the starting point. If the speed of the boat is 4 miles per hour in still water, what is the rate of the current

Answer 1

Let the speed of the water current be v.

 

 

total travel time = time to go upstream + time to return downstream to the starting point

 

Hence, 8 = time in hours =  6 / (4-v) + 6 / (4 +v)  = 6*8/(16-v^2)

 

Hence, 16 - v^2 = 6, or v^2 = 10 or v = √10 miles / hour