Amotorboat traveling with the current went 80 miles in 4 hours. against the current, it took 5 hours to travel the same distance. find the rate of the motorboat in calm water.

Let x be the speed of the motorboat and y be the speed of the current.

Then, for downstream, the speed is x + y.

Now, speed = distance/time.

Distance = 80 miles.

Time for downstream = 4 hours.

So, x + y = 80/4 = 20     (1)

Against the current, that is for upstream, the speed is x - y.

Time for upstream = 5 hours.

x - y = 80/5 = 16     (2)

Adding (1) and (2), we get,

2x = 36

x = 18

Hence, rate of the motorboat in calm water = 18 miles/hour.