PP2 PS68

[sht]

In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?

I. 0<t<h
II. c<t<h
III. c/2<t<h/2

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III


答案是E
請問為什麼III對？

[christinehsu]

這題我是帶數字進去算的，
你參考看看，我也不確定我的想法對不對。
設C=2 H=3----->T=6/5
III. c/2<t<h/2
代數字進去
2/2<6/5<3/2

希望大家多討論。
謝謝

[alima309]

漏水的速度c快h慢
如果一起漏的話 t 最快
所以0<t<c<h

對於漏水速度較快的c而言, 加入h 這個洞 速度一定小於2倍的c
反之亦然

把漏水速率反過來就變成時間了