求助, OG 数学DS 173

pipa66

173. The figure above represents the floor plan of an art gallery that has a lobby and 18 rooms. If lisa goes from the lobby into room A at the same time that Paul goes from the lobby into room R, and each goes through all of the rooms in succession, entering by one door and exiting by the other, which room will they be in at the same time?

1. Lisa spends 2x minutes in each room and Paul spends 3x minutes in each room
2. Lisa spends 10minutes less time in each room than Paul does.

本题有图示的不过太复杂, 我实在画不出. 各位帮忙对照OG帮我看一下吧...... 我看到这题就不知从和下手, OG的解释太复杂,我理解不了....

先谢谢了

sammen

身边没有OG,帮你顶.PS:数学做OG帮助不大.

himba

条件一：L的速度为1/2x，P的速度为1/3x，那么两个相遇时的时间为18/(1/2x+1/3x)=108x/5，相遇时L走的房间数=1/2x*108x/5=10.8，所以两人将在第11个房间相遇。
条件二：未给出两个的速度，无法判断。
因此，A。

teyvhf

关键是找到两个等量关系：

a）在相遇时，L和P走的时间相等 -〉 L速度*L房间数=P速度*P房间数
b）由于两人是相向而行，走的总房间数是18 -〉L房间数+P房间数=18

看条件：
1) 把2x 和 3x 代入等式a -> 2 * L房间数 = 3 * P房间数. 加上条件b, 解一个2元1次方程。成立。
2）设L速度=x, P速度=x+10, 求不出来。