A raft and a motorboat simultaneously leave from the same point and move down the river. After 2 hours the motorboat turns around and starts moving towards the raft. How many hours will they move towards each before meeting?
Answer:2 hoursStep-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 mphIn two hours they will cover: motorboat = 2(x+y) miles raft = 2y milesAfter 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 milesThe 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]