Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio Q of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job? Choose the correct choice from the following answers:
A) 5 to 1	B) 10 to 7	C) 1 to 5	D) 7 to 10	E) 9 to 10
Solutioning this exercise can be facilitated by using a R T W (rate time work) table:   We translate the exercise into the table:   R T W   X t/2 1   Y t 1   Z (t/2*3/2 =3t/4) 1   From this table we find the rates   Rx = 2/t   Ry = 1/t   Rz = 4/3t   The Q is what is the ratio of (Tx + Ty) / (Ty + Tz)   Rx + Ry = 2/t + 4/3t = 6/3t+4/3t = 10/3t   Ry+Rz = 1/t + 4/3t = 3/3t + 4/3t = 7/3t   The (10/3t)/(7/3t) = 10/7 then the work ratios is 10 to 7   Since Time Ratio Q is the inverse of work, the the answer is 7 to 10   CORRECT ANSWER 7 to 10
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Machine X can complete a job in half the time it takes Machine Y to complete the same job, and Machine Z takes 50% longer than Machine X to complete the job. If all three machines always work at their respective, constant rates, what is the ratio Q of the amount of time it will take Machines X and Z to complete the job to the ratio of the amount of time it will take Machines Y and Z to complete the job?