GMAT Focus EditionQuantitative ReasoningMedium
A production line has two machines, A and B. Machine A can produce 100 units in 5 hours. Machine B can produce 150 units in 6 hours. If both machines work together for 3 hours, how many units will they produce?
- A140 units
- B130 units
- C135 units
- D125 units
Show answer & explanationAnswer & explanation
Correct answer: C. 135 units
First, calculate the individual production rates: Machine A is 100 units / 5 hours = 20 units/hour. Machine B is 150 units / 6 hours = 25 units/hour. Their combined rate is 20 + 25 = 45 units/hour. If they work together for 3 hours, they will produce 45 units/hour * 3 hours = 135 units.
Why the other options are wrong
- A. This could occur if one machine's rate was slightly off or if there was a calculation error.
- B. This could be a miscalculation of the combined rate multiplied by time.
- D. This might come from errors in calculating individual rates or the combined total.
Combined Work Rate (Production)
The total output rate when multiple machines or workers produce items together, calculated by summing their individual production rates.
- Individual rate = Total units / Time taken.
- Combined rate = Sum of individual rates.
- Total production = Combined rate × Time worked.
Memory trick: Each machine has its own speed; together, they add up!