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 machine 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?
18
13~$\frac{1}{2}$~
7~$\frac{1}{5}$~
4~$\frac{1}{2}$~
3~$\frac{2}{3}$~
设工作为1
X的速率是1/9每小时
3/9+ 4(1/9 + 1/Y) = 1
1/Y = 1/18
设那项工作为1,Y需要T小时独自完成那项工作
X的速率为 1/9,Y的速率为 1/T
7*1/9 + 4*1/T = 1
T = 18