Q26:

Running at their respective constant rates, machine X takes two days longer to produce W widgets than machine Y. At these rates, if the two machine together produce 5/4W 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

答案是 E. 请教思路. 多谢!!

(5/4)/(1/x+1/(x+2))=3==>x=6,x=5/4

2/(1/6)=12

设Xmachine X天完成，Ymachine X+2天完成，效率分别是1/x,1/x+2

仅供参考

think of this as a rate problem like ztlbox suggested, so the quesiton becomes "x can finish a job 2 days longer than y can; and a job 5/4 the size would take both x and y together 3 days to finish; so how long would x finish a job twice as big by itself?"

if x machine can finish the job in x days, then y machine can finishe the job in x-2(not x+2), and the rates are 1/x and 1/x-2;

so we know that ( 5/4 ) / (1/x + 1/x-2) = 3, so we get 5*(x^2 - 2x) = 12*(2x - 2) => 5x^2 - 34x + 24 = 0 => (5x - 4)(x - 6) = 0 => x = 4/5 or x = 6, since 1/x can not be greater than 1, then x = 6 and 1/x = 1/6 and thus 2/(1/x) = 12;