奧數 15點 - Ans.fyi 參考答案

奧數 15點

2010-08-26 1:30 am

1) 一工程隊修建一條公路,當任務完成10%時,採用新設備,修路速度提高20%,每天工作時間縮短為原來的85%,結果167天完成。原計劃多少天完成?

2)甲、乙兩人同時從A、B兩地相向出發,甲的速度是乙的速度的1.5倍,到達對方出發點後立即返同,如果第一次相遇點和第二次相遇點相距300米,那麼,A、B兩地的距離為多少米?

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更新1:

最好一次答兩題! Thx!

回答 (1)

[匿名]

2010-08-26 1:52 am

✔ 最佳答案

I can't type Chinese. Sorry about that.

1) Let t be the time of the original plan.

[(1-10%)t] / [(1+20%)(85%)] = 167
0.9t / 1.02 = 167
t = 189

'.' The time of the original plan is 189 days.

2010-08-25 18:12:09 補充：
2) The speed of 甲 : The speed of 乙 = 3:2
Let 5k be the distance between A and B.
甲 run 3k and 乙 run 2k.
A 3k 2k B
-----------------------------[1]-------------------
甲&乙meet at point [1]

2010-08-25 18:12:16 補充：
甲 run 9k and 乙 run 6k
A 1k 2k 2k B
---------[2]----------------[1]------------------
甲&乙meet at point [2]
distance between point [1] and point [2] = 2k = 300m
k = 150m
5k = 750m
'.' the distance between A and B is 750m

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