A boat going in the river downstream went 30km in 2 hours. The same boat going upstream reaches the same distance after 6 hours. The river flow speed and the boat's speed are constant throughout the whole journey. What is the river flow speed?

1 Answer
Feb 4, 2018

The river flow speed is 5km/h

Explanation:

Let's call the boat's speed B and the river's speed R. The movement downstream lets us know that the sum of the speeds gets us 30km in 2 hours or a speed of 15 km per hour (30/2), so:

#B + R = 15#

The movement upstream tells us that the boat's speed minus the river's speed lets the boat do the same distance fo 30 km in 6 hours so a total speed of 5 km per hour (30/6), which gives us:

#B - R = 5#

Armed with these two equations we can sum each of the terms so we get:

#(B+B)+(R-R)=15+5#

#2B=20#

#B=10#

So the boat's speed is 10km/h and when you plug 10 into any of the two equations you will get that the river's speed is 5km/h.