Question 1024868
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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/x}}},  while the rate-of-work of the faster machine is  {{{1/(x-2)}}}.

The combined rate of two machines working together is  {{{1/x}}} + {{{1/(x-2)}}}.

According to the condition,

{{{1/x}}} + {{{1/(x-2)}}} = {{{1/((12/5)))}}}.    ( <--- {{{12/5}}} = {{{2}}}{{{2/5}}} hours = 2 hours and 24 minutes)

Or

{{{1/x}}} + {{{1/(x-2)}}} = {{{5/12}}}.

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^2 - 10x}}}.

{{{5x^2 - 34x + 24}}} = {{{0}}}.

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

<U>Answer</U>. 6 hours.
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