Answer: the speed of the current is 2.5 mph
Step-by-step explanation:
Let the speed of the boat be x miles per hour
Let the speed of the current be y miles per hour
Speed = distance / time
Time = distance/speed
If the boat goes 12miles downstream(in still water) at 15 mph then, the time is
12/ 15 = 0.8 hours
In still water, it means that it moved in the same direction with the current.
The total speed would be x + y. Therefore
x + y = 15 - - - - - - -1
If the boat goes 8 miles upstream in 0.8 hours, the the speed is
8/ 0.8 = 10 miles per hour
Assuming it moved in the opposite direction to the current.
The total speed would be x -y. Therefore
x - y = 10 - - - - - - -2
Adding equation 1 and equation 2, it becomes
2x = 25
x = 25/2 = 12.5
y = 15 - x
y = 15 - 12.5 = 2.5 miles per hour
