machine 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 1/2 C)7 1/5
I noticed that not all of the answer choices were listed. I think the answer is 12. If not, will someone tell me why we couldn't solve the prob this way:
x rate = 1/9, x works for 3 hrs and completes 1/3 of the work.
now, x and y wrapped up the remaining 2/3 of work in 4 hrs:
r(4)=2/3 ==> r = 2/3(1/4) = 2/12 = 1/6.
so, x's rate is 1/9 and x's and y's combined rate is 1/6. in order to find y's rate let's subtract 1/9 (x's rate) from 1/6 (x's and y's combined rate)
1/6 - 1/9 = 1/18. 1/18 is y's rate. the prob asks: How many hours would it have taken machine y working alone to complete
the entire job? so, 1/18t=2/3 ==> t=36/3 = 12.
What do you all think? Any probs w/this?