求教一道数学题，大家帮帮我吧

Maggie草 · 发表于 2011-3-20 22:31:49

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

sdcar2010 · 发表于 2011-3-20 22:53:33

Let's suppose that X produce w in A days. Then Y produce w in (A-2) days.

Therefore:
3*(w/A +w/(A-2)) = 5w/4; and A is bigger than 2.

5A^2 -34A + 24 = 0

So A =6

Then to produce 2w, X needs 2A or 12 days.

crystalzozo · 发表于 2011-3-20 22:54:42

设Y完成的天数为y,则X完成的天数为y+2
Y的速度为W/y, X的速度为W/(y+2)
3*(W/y)+3*W/(y+2)=W*5/4
得到y=4,y=-5/6(舍）
则X的天数为6，X的速度为W/6
2W/(W/6)=12
选E

Maggie草 · 发表于 2011-3-22 22:09:41

谢谢楼上两位

小唯唯 · 发表于 2011-4-30 10:17:48

很是清楚啊~

求教一道数学题，大家帮帮我吧

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