SOLUTION: A new printing machine can do a job in 6 hours. An old machine can complete the same job in 16 hours. If 3 new machines and 4 old machines are used to do the job, how many hours

Question 1154934: A new printing machine can do a job in 6 hours. An old machine can complete the same job in 16 hours. If 3 new machines and 4 old machines are used to do the job, how many hours will be required to finish?
Found 2 solutions by ikleyn, jim_thompson5910:
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
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The new machine makes of the job per hour. The old machine makes of the job per hour. 3 new machines and 4 old machines do + of the job per hour. + = + = of the job per hour. Hence, it will take hours to complete the job, or hours = 1 hour and 20 minutes. ANSWER

Solved.

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

The lowest common multiple of 6 and 16 is 48
You can list out the multiples of 6 and 16 to see this, or you can multiply 6 and 16 to get 6*16 = 96, then divide by the GCF 2 to get 96/2 = 48.

Let's say we need to print 4800 pages. This is just some fairly large number. I started with 48 and tacked on two zeros. You'll see why in a moment.

If a new machine can do the job in 6 hours, then it can print at a rate of 4800/6 = 800 pages per hour. In other words, after 1 hour, there are 800 pages printed.

The old machine can print at a rate of 4800/16 = 300 pages per hour. After 1 hour, there are 300 pages printed.

If the two machines work together, then we have 800+300 = 1100 pages printed after 1 hour. This is assuming one machine does not hinder the other.

Now let's consider the fact we have 3 new machines and 4 old ones.
1 new machine works at a rate of 800 pgs per hr
3 new machines work at a rate of 2400 pgs per hr (multiply by 3)
1 old machine works at a rate of 300 pgs per hr
4 old machines work at a rate of 1200 pgs per hr (multiply by 4)

In total, the seven machines combine to an overall rate of 2400+1200 = 3600 pages per hour.

Let x be the number of hours it takes to get the job done. The "job" in this case is printing 4800 pages.

We multiply the rate by the number of hours to figure out how many pages we can get done in that time
(rate)*(number of hours) = number of pages printed
(3600 pgs per hr)*(x hours) = 4800 pgs
3600x = 4800
x = 4800/3600
x = 48/36
x = (12*4)/(12*3)
x = 4/3
x = 1.333 hours approximately
x = 1 & 1/3 hours
Since 60 min = 1 hour, this means 20 min = 1/3 hour (divide both sides by 3)
Therefore,
1 & 1/3 hr = 1 hour, 20 minutes = 1 hour + 20 min = 60 min + 20 min = 80 min

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Answer: Approximately 1.333 hours
This is equivalent to 1 hour, 20 minutes
In terms of minutes only that is equivalent to 80 minutes

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