Amotorboat used as a river taxi can travel at 8 mph in calm water. the amount of time it takes to travel 9 miles against the current is the same amount of time it takes to travel 15 miles with the current. what is the rate of the current?

Hello

1) Let's call  the velocity of the motorboat in calm water. When it travels against the current, the relative velocity will be , where  is the current velocity. Similarly, when the motorboat travels with the current, its relative velocity will be . 

2) Given , where  is the relative velocity, when the motorboat travels against the current the time to cover a distance of  is 

Similarly, when the motorboat travels with the current, the time to cover a distance of   is 


3) The problem says that these two times are equal. So we can write:

And we can solve this to find , the current rate: