Machines X and Y run at different constant rates, and machine X can complete a certain job in 9 hours

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?
18
13+1/2
7+1/5
4+1/2
3+2/3











First we need to find the rate together:
let T = time it takes for X and Y to complete one job together in hours
3 hrs * (1 job / 9 hrs) + 4 hrs * (1 job / T hours) = 1 job
T = 6
Rate of X + Rate of Y = Rate Together
1/9 + 1/Y = 1/T
1/9 + 1/Y = 1/6
Y = 18
ANSWER: A. 18 hours