The effective speed downstream is  = 24 miles per hour.

It is the sum of the motorboat own speed relative to water and the current speed:


24 = u + v     (1)


The effective speed upstream is  = 16 miles per hour.

It is the difference of the motorboat own speed relative to water and the current speed:


16 = u - v.    (2)


Thus you have these two equations

u + v = 24
u - v = 16


Add them to get

2u = 24 + 16 = 40  ====>  u = 40/2 = 20


and then from eq(1)  get  v = 24 - 20 = 4.


Answer.  The rate of the current is  4 miles per hour.