Five machines at a certain factory operate at the same constant rate. If four of these machines,...

Question

Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 30 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?

GMAT Panda · Accepted Answer

6 We name R as the rate of one machine in orders per hour and Q as the total size of the production order. Q = 4 R 30 We calculate the time T required for five machines working together to complete Q. 5 R T = Q T = Q/5 R T = 4 R 30/5 R T = R 4 305 R T = 120/5 T = 24 We compute how many fewer hours five machines save compared to four machines. 30 - 24 = 6

Explanation	Calculations	Help
$We name R as the rate of one machine in orders per hour and Q as the total size of the production order.$	$Q = 4 \times R \times 30$
$We calculate the time T required for five machines working together to complete Q.$	$5 \times R \times T = Q T = \frac{Q}{5 \times R} T = \frac{4 \times R \times 30}{5 \times R} T = \frac{R \times 4 \times 30}{5 \times R} T = \frac{120}{5} T = 24$
$We compute how many fewer hours five machines save compared to four machines.$	$30 - 24 = 6$

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