Working alone, printers X, Y, and Z can do a job in 12 hrs, 15 hrs and 18 hrs respectively.
What is the ratio of the time it takes X to do a job alone, to the time it takes Y & Z to do the job together.
I came up with 15:22
ETS says 22:15. If I'm wrong, please correct me
2006-12-10 13:11:48 · 5 answers · asked by Jason A 1 in Science & Mathematics ➔ Mathematics
The answer is really 22:15.
The rate for X alone is 15hrs. per job, and the rate it takes Y and Z together is 90/11 hrs. per job.
The latter rate is arrived at by setting up an equation,
given the following:
h = # hours it takes Y and Z together to do the job,
1/15 = the amount of the job that Y completes in one hour
1/18 = the amount of the job Z completes in one hour
(so that (1/15 + 1/18) indicates the part of the job that Y and Z complete in one hour)
the equation is
h(1/15 + 1/18) = 1 (The "1" means "one whole job.")
Solving this equation gives h = 90/11, the number of hours it takes Y and Z together to do one job.
The ratio 12:(90/11) simplifies to 22:15.
2006-12-10 13:39:25 · answer #1 · answered by susan els 1 · 1⤊ 0⤋
Printer X can do the job in 12 hours.
Y can do 1/15 of the job in 1 hour.
Z can do 1/18 of the job in 1 hour.
So together, they do 1/15 + 1/18 = 11/90 of a job in 1 hour.
Which means they can do the job in 90/11 hours.
The ratio is thus 12:90/11
Dividing through by 6 gives 2:15/11
Multiplying through by 11 gives 22:15.
2006-12-10 13:53:03 · answer #2 · answered by falzoon 7 · 0⤊ 0⤋
They're right. Ok, firstly, think of it intuitively - if one machine does the job in 15 & another in 18, then surely, combined they must do the job quicker than 15 hours, right?
Classic GMAT problem. the quickest way to do these "combined work" problems (sans calculator) is to find a common denominator, then figure out the hourly rate. In this case, 90 works (15 & 18 both go into 90 evenly). So, say one printer churns out 90 pages in 15 hours, another does it in18 hours, Get the hourly rate for each (one is 6 pages per hour, another is 5 pages per hour). So, combined, they now churn out 11 pages per hour. They get the job of 90 done now in 90/11 hours (or 8.1818..).
The ratio is then 12: (90/11) = 11*12/90 = 11*2*6/(6*15) = 22/15
2006-12-10 13:38:16 · answer #3 · answered by Buhlmann 2 · 0⤊ 0⤋
It is 22:15. It takes y and z 90/11hrs to do it together, so 12/(90/11) = 22/15.
2006-12-10 13:19:09 · answer #4 · answered by doverbeach 3 · 1⤊ 0⤋
Wouldn't X alone take longer? So shouldn't the bigger number be first?
2006-12-10 13:17:10 · answer #5 · answered by Kerry S 2 · 0⤊ 1⤋