题目信息
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?
A:18
B:13
C:7
D:4
E:3
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已选答案：
正确答案：
A:18
Algebra Applied problems
Machine X can complete the job in 9 hours, so it completed
of the job before machine Y started working. Since machine X worked 4 more hours, it completed 
of the job, which left 
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 
= 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 
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 
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 
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,
The correct answer is A.
Machine X can complete the job in 9 hours, so it completed
of the job before machine Y started working. Since machine X worked 4 more hours, it completed of the job, which left 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 = 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 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 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 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,The correct answer is A.
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