A boat can travel 24 miles in 3 hours when traveling with a current. Against the same current, it can travel only 16 miles in 4 hours. Find the rate of the current and the rate of the boat in still water.

The current speed of the river is 2 miles / h while the speed of the boat is 6 miles/h.

Step-by-step explanation:

When the boat is travelling with the current it's relative speed can be calculated by the speed of the boat plus the speed of the current on the other hand when the boat is travelling against the current the relative speed will be the speed of the boat minus the speed of the current, since the average speed is the distance divided by the time, we have:

With the current:

speed = distance / time

speed = 24/3 = 8 miles/h

boat_speed + current_speed = 8 miles/h

Against the current:

speed = distance/time

speed = 16/4 = 4 miles/h

boat_speed - current_speed = 4 miles/h

Since we have two equations and two variables we can solve them through a system of equations. For that we will isolate the boat_speed on the first equation and use that expression on the second equation to solve for the current_speed. This is shown bellow:

boat_speed = 8 - current_speed

(8 - current_speed) - current_speed = 4

8 - 2*current_speed = 4

-2*current_speed = 4 - 8

-2*current_speed = - 4

current_speed = 4/2 = 2 miles/h

We can now solve for the boat speed, we have:

boat_speed = 8 - 2 = 6 miles/h

The current speed of the river is 2 miles / h while the speed of the boat is 6 miles/h.