Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A production manager is monitoring machine efficiency. Machine A produces 120 units in 45 minutes. Machine B produces 160 units in 1 hour. Which machine has a higher production rate, and by how many units per hour?
- AMachine A, by 10 units per hour
- BMachine A, by 20 units per hour
- CMachine B, by 10 units per hour
- DMachine B, by 20 units per hour
Show answer & explanationAnswer & explanation
Correct answer: B. Machine A, by 20 units per hour
Convert all production rates to units per hour. For Machine A: 40 minutes = 40/60 = 2/3 hours. Production rate for A = 120 units / (2/3 hours) = 120 * (3/2) = 180 units/hour. For Machine B: 1 hour. Production rate for B = 160 units / 1 hour = 160 units/hour. Machine A produces 180 units/hour, and Machine B produces 160 units/hour. Machine A has a higher rate by 180 - 160 = 20 units per hour.
Why the other options are wrong
- A. Correctly identifies Machine A as faster, but calculates the difference incorrectly.
- C. Incorrectly identifies Machine B as faster and calculates the difference incorrectly.
- D. Incorrectly identifies Machine B as faster and calculates the difference.
Rate Comparison (Unit Rate)
Comparing the efficiency or speed of different entities by converting their performance to a consistent unit rate (e.g., units per hour, miles per gallon).
- Ensure all quantities are in comparable units.
- Calculate the 'per unit' value for each item.
- Directly compare the calculated unit rates.
Memory trick: Standardize the time, then rate the climb!