Answer:
2 hours
Step-by-step explanation:
Let x mph be the speed of motorboat in still water and y mph be the speed of current.
A raft and a motorboat simultaneously leave from the same point and move down the river, then speeds down the river are:
motorboat = x + y mph
raft = y mph
In two hours they will cover:
motorboat = 2(x+y) miles
raft = 2y miles
After 2 hours the motorboat turns around and starts moving towards the raft (against the current), so its speed is now x - y mph.
Let t be the time they move towards each other. In t hours, they cover
motorboat = t(x - y) miles
raft = ty miles
The distance from the starting point to the turning point is the same as the sum of the distances the raft covers and the motorboat covers after turning around, so
[tex]2(x+y)=2y+t(x-y)+ty \\ \\2x+2y=2y+tx-ty+ty\\ \\2x=tx\\ \\t=2\ hours[/tex]
