Q26:

Running at their respective constant rates, machine X takes 2 days longer to produce w widgets than machine Y.  At these rates, if the two machines together produce 5/4 w widgets in 3 days, how many days would it take machine X alone to produce 2w widgets?

A.      4
   

B.      6

C.      8

D.     10

E.      12

我想到個比較煩但易明的方法,不知大家怎看?

先找c看,2wx=8,wx=4>wy=2, 不行,因x+y也要3days.

d:wx=5>wy=3,同樣不行,因x+y也要3days

e:wx=6>wy=4,在這題唯一可用答案.

设machine x和y的生产速度分别为x、y个widget/day,

根据题干有

w/x-w/y=2

3x+3y=5/4w

求2w/x

令m=w/x,n=w/y

转化为

m-n=2

将m=n+2代入3/m+3/n=5/4经化简得5n^2-14n-24=0,(n-4)(5n+6)=0,得n=4或-6(舍去）

所以m=n+2=6,2m=12

选E