數學題請教

2012-08-12 11:37 pm
數學題請教:
A man arranges with his wife to pick her up at the bus station at 11am. Howevershe finishes her shopping at 10am,and decides to start walking home. Later her husband meets her on the road, picks her up and drives back home. They arrivehome 30 mins earlier than if she had waited. At what time did her husband pick her up?

回答 (1)

2012-08-13 6:15 am
✔ 最佳答案
設d是巴士站與家的距離,而v是車的速度

首先當那個巴士站就在市場面口,以下是圖解


home ‧.................................‧pick up point ............. ‧Bus stop

T1 11a.m.
T1-30 T2 10a.m.


從圖看,若他的丈夫按原定的計劃於11a.m.在巴士站接她的話,他們會在T1到家

因此 (T1-11).v=d ------------(1)

設 d2 = pick up point和家的距離,而d1=pick up point和巴士站的距離

d2=(T1-0.5-T2).v 而 d1=(11-T2).v (因他預算11a.m.到達,但於T2遇上,故11a.m. - T2就是他由pick up point駛去巴士站的時間)

d=d1+d2

(T1-11).v = (T1-0.5-T2).v + (11-T2).v
T1-11 = T1-0.5-T2 + 11 - T2
2T2 = 22-0.5
T2 = 10.75 =10時45分

希望幫到你!


2012-08-12 22:17:24 補充:
對不起,圖的空格吃了

如下:
home ‧.................................‧pick up point ............. ‧Bus stop

T1  ‧..........................................................................‧ 11a.m.
T1-30 ‧...................................... T2 .................................. 10a.m.


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