SOLUTION: Two printing machines are working together to complete printing question papers for examination in 2hours and 24 minutes. When one machine is printing alone it takes 2hours longer

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Question 1024868: Two printing machines are working together to complete printing question papers for examination in 2hours and 24 minutes. When one machine is printing alone it takes 2hours longer than the other. How long does the slowe machine take?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
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Two printing machines are working together to complete printing question papers for examination in 2 hours and 24 minutes.
When one machine is printing alone it takes 2 hours longer than the other.
How long does the slower machine take?
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Let x be the time the slower machine takes. Then the faster machine will take (x-2) hours.

Thus the rate-of-work of the slower machine is  1%2Fx,  while the rate-of-work of the faster machine is  1%2F%28x-2%29.

The combined rate of two machines working together is  1%2Fx + 1%2F%28x-2%29.

According to the condition,

1%2Fx + 1%2F%28x-2%29 = 1%2F%28%2812%2F5%29%29%29.    ( <--- 12%2F5 = 22%2F5 hours = 2 hours and 24 minutes)

Or

1%2Fx + 1%2F%28x-2%29 = 5%2F12.

It is your equation for x. To solve it, multiply both sides by 12*x*(x-2). You will get

12(x-2) + 12x = 5x*(x-2).

Now simplify and solve it:

12x - 24 + 12x = 5x%5E2+-+10x.

5x%5E2+-+34x+%2B+24 = 0.

Apply the quadratic formula and find the positive root x = 6.

Answer. 6 hours.