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  3. Machines X and Y run at different constant rates，and machine X can complete a ce

Machines X and Y run at different constant rates，and machine X can complete a ce

游客2025-02-27  19
问题 Machines X and Y run at different constant rates，and machine X can complete a certain job in 9 hours． Machine X worked on the job alone for the first 3 hours and the two machines，working together，then completed the job in 4 more hours．How many hours would it have taken machine Y, working alone，to complete the entire job?
选项 A、18
B、
C、
D、
E、
答案 A
解析 Machine X can complete the job in 9 hours, so it completed 1/3 of the job before machine Y started working. Since machine X worked 4 more hours, it completed 7/9 of the job, which left 2/9 of the job for machine Y to do during the 4 hours it worked together with machine X to complete the job. At this rate, machine Y would take (2/9) (4) = 18 hours to do the entire job working alone.
Alternatively, machine X can complete the job in 9 hours, so it completed — of the job before machine Y started working. This leaves 2/3 of the job, which took machines X and Y, working together, 4 hours to complete. So, if working together the machines took 4 hours to complete 2/3 of the job, it would take them 6 hours to do the whole job working together. Furthermore, rates are additive, so we should convert working times to rates. Machine X’s rate is — jobs per hour. Both machines together have a rate of 1/6 jobs per hour.
We must determine machine Y’s individual rate — for the whole job. First, add machine X’s rate to machine Y’s rate to get the combined rate. Then,
4/9+1/Y=1/6
    1/Y=1/6-1/9
    1/Y=2/36
     Y=18  
The correct answer is A.
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