GMAT Practice Question: 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?
- 3
- 5
- 6
- 16
- 24
Topics: word problems, rates
Solution
Step 1
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
Step 2
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{\cancel{R} \times 4 \times 30}{5 \times \cancel{R}} T = \frac{120}{5} T = 24
Step 3
We compute how many fewer hours five machines save compared to four machines.
30 - 24 = 6
Answer
6
