Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityHard
A production manager is analyzing machine output. Machine A produces 120 units in 3 hours. Machine B produces 150 units in 4 hours. Which machine has a higher production rate, and by how many units per hour?
- AMachine B, by 2.5 units per hour
- BMachine A, by 2.5 units per hour
- CMachine B, by 5 units per hour
- DMachine A, by 5 units per hour
Show answer & explanationAnswer & explanation
Correct answer: B. Machine A, by 2.5 units per hour
Calculate the unit rate for each machine. Machine A: 120 units / 3 hours = 40 units/hour. Machine B: 150 units / 4 hours = 37.5 units/hour. Machine A has a higher rate. The difference is 40 - 37.5 = 2.5 units/hour.
Why the other options are wrong
- A. Incorrect machine and incorrect difference.
- C. Incorrect machine and incorrect difference.
- D. Incorrect difference in rates.
Comparing Unit Rates
To compare two different rates, calculate the unit rate for each scenario (amount per one unit of time, quantity, etc.). Then, directly compare these unit rates to determine which is higher or lower.
- A unit rate expresses a quantity per single unit of another quantity.
- Comparison requires both rates to be in the same 'per unit' format.
- The difference between unit rates indicates the magnitude of the disparity.
Memory trick: Each rate, then compare. Divide, then subtract.