Two ferries start at the same time from opposite sides of a river.Each travels at a constant speed,but one is faster than the other .They pass at a point 720m from the nearest shore.Both boat wait ten minutes before going back.On the return trip they

Question

Two ferries start at the same time from opposite sides of a river.Each travels at a constant speed,but one is faster than the other .They pass at a point 720m from the nearest shore.Both boat wait ten minutes before going back.On the return trip they meet 400m from the other shore .
How wide is the river

Answer 1

已知：两船匀速渡河,其中一船速度快,相遇时距最近河岸720m；渡河后各停留10min后回返,再次相遇时,距另一河岸400m.
求：河宽.
假设：起初,A船从河A岸出发,B船从河B岸出发,A船速度V(A)大于B船速度V(B)；且河岸宽L.
解题过程如下：
两次相遇时,A、B两船行驶时间相同.
第一次相遇,因为V(A)＞V(B)；所以A船驶过的距离长,所以第一次相遇点（设为1点）距离B岸更近,所以1点距B岸距离为720m,此即为B船驶过的距离；根据两船行驶时间相同,有如下等式：（L-720)/V(A) = 720/V(B)；
第二次相遇,是在A船到达对岸（B岸）,停泊10min,回返A岸的途中,此时B船也在A岸停泊10min后正在回返B岸,根据题中意思,相遇点（设为2点）距A岸400m,此时B船正从A岸回返B岸,因此,此(L+400)m是B船行驶过的距离,同理,可知A船经过的距离为(L+L-400)m；由于从起初行船至今,两船行驶时间相等,有如下等式：
(L+L-400)/V(A) = (L+400)/V(B)
将以上两等式联立,消去V(A) 、V(B) ,解出L值.
L = 1760m.