GMAT Focus EditionQuantitative ReasoningEasy
A factory has two production lines, Line P and Line Q. Line P produces 100 units per hour. Line Q produces 150 units per hour. If both lines operate simultaneously, how many hours will it take to produce a total of 1250 units?
- A4 hours
- B5 hours
- C6 hours
- D7 hours
Show answer & explanationAnswer & explanation
Correct answer: B. 5 hours
When two production lines operate simultaneously, their rates combine. Line P's rate is 100 units/hour, and Line Q's rate is 150 units/hour. Their combined rate is 100 + 150 = 250 units/hour. To find the time taken to produce 1250 units, divide the total units by the combined rate: 1250 units / 250 units/hour = 5 hours.
Why the other options are wrong
- A. This would be 1000 units at 250 units/hour.
- C. This would be 1500 units at 250 units/hour.
- D. Incorrect calculation.
Combined Work Rate
When multiple entities (people, machines, etc.) work together on a task, their individual work rates are added to find the combined work rate. The time taken is then total work divided by the combined rate.
- Rates are additive when working together.
- Work = Rate × Time.
- Time = Work / Combined Rate.
Memory trick: Rates Add Up, Work Gets Done Faster.