SOLUTION: A printing press can print 300,000 cards in 12 hours. An older press requires 18 hours to print 300,000 copies of a card. How long would it take for both presses working together t

Question 248812: A printing press can print 300,000 cards in 12 hours. An older press requires 18 hours to print 300,000 copies of a card. How long would it take for both presses working together to print 300,000 copies?

I need the rate of work (R), the time of work (T) , and the work done (W)
the equation is RT = W.
It would help if I am provided a detailed explanation
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
Formula is RT = W

From this formula, you can derive:

T = W/R
and
R = W/T

printing press can print 300,000 cards in 12 hours.

T = 12
W = 300,000
R = W/T = 300,000/12 = 25,000 cards per hour.

older press requires 18 hours to print 300,000 cards.

T = 18
W = 300,000
R = W/T = 16,666.66666667 cards per hour.

working together, their rates will combine.

you get:

T = x
W = 300,000
R = 25,000 + 16,666.66666667 = 41,666.66666667 cards per hour.

When solving for T, formula becomes:

T = W/R

This equation becomes:

T = 300,000/41,666.66666667 = 7.2 hours.

In 7.2 hours, the printing press has completed 25,000 * 7.2 = 180,000 cards.

In 7.2 hours, the old press has completed 16,666.66666667 * 7.2 = 120,000 cards.

total cards produced is 180,000 + 120,000 = 300,000
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