又一道绕来绕去的题

又一道绕来绕去的题，看到我头晕。

Q28:

This year Henry will save a certain amount of his income, and he will spend the rest.  Next year Henry will have no income, but for each dollar that he saves this year, he will have 1 + r dollars available to spend.  In terms of r, what fraction of his income should Henry save this year so that next year the amount he was available to spend will be equal to half the amount that he spends this year?

答案说是1/（2r+3)

请知道的说说怎么算的，谢谢！

假设花掉的钱是x，存的钱y，那么第二年花的钱是y(1+r)

得到 x=2y(1+r)

x/y=2+2r

x/y+1=3+2r

(x+y)/y=3+2r

y/(x+y)=1/(3+2r)

假设存的fraction = x, 那么花的为 1-x,

第二年存的增长到 x (1+r), 按题目说，这个数值为第一年花的1/2

x(1+r) = (1-x)/2

解的 x = 1/(3+2r)

谢谢啊，还是英文底子差闹的，不好意思。

还有一道迷糊的：

Q12:

Working alone at its constant rate, machine K took 3 hours to produce 1/4 of the units produced last Friday.  Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday.  How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?

A.     8

B.      12

C.      16

D.     24

E.      30

我是不理解：既然前面说了1台3小时做1/4，那么就是说1小时做1/12，所以12小时应该就完成了。

后面说3台一起6小时做剩下的，是3/4吧？那么这么算下来是1台6小时做1/4，需要24小时才完成。哪里出错了呢？请指点。

一共才两台机器。 Machine K 和 Machine M

Machine K 单独作需要 3/(1/4) = 12 小时， Machine M 需要 m 小时

(1/12+ 1/m)* 6 = (1-1/4) ，解得 m = 24 小时

惭愧惭愧，题目看的马虎，谢谢cloudymind!