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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 , while the rate-of-work of the faster machine is .
The combined rate of two machines working together is + .
According to the condition,
+ = . ( <--- = hours = 2 hours and 24 minutes)
Or
+ = .
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 = .
= .
Apply the quadratic formula and find the positive root x = 6.
Answer. 6 hours.