求救一道GWD

精灵宝宝

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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

heygika

E?

精灵宝宝

对 怎么算的？

heygika

设y单独完成的天数是y, 则x的天数是y+2
y的速度是1/y, x的速度是1/(y+2)

[1/y+1/(y+2)]*3=5/4 -->y=4
那x单独完成1w widgets需要6天 (4+2)
完成2w需要12天.


如果不想算的话,可以这样想:
x和y共同用了3天完成5/4w.
x比y慢2天, 说明y完成了3/4w，x完成了2/4w
那么完成2w的话,x就应该是12天.

gvonvon

设Y用m天做w,则X用m+2天
(1/(m+2) +1/m) *3=5/4
解出m=4
所以2w/(4+2)=12