Unit Rate and Ratios: TEAS Practice Question with Answer & Explanation

Understanding Unit Rates and Time Conversion

In the TEAS Math section, calculating unit rates is a fundamental skill. A unit rate is a ratio where the second term is 1. When the question asks for the rate "per hour," your goal is to determine how far the traveler would go in exactly 60 minutes.

Step-by-Step Calculation

To solve this problem, we need to convert the travel time from 20 minutes into 1 hour (60 minutes). There are two primary ways to approach this:

1. The Multiplication Method:

   • We know there are 60 minutes in 1 hour.
   • Determine how many 20-minute segments are in one hour: $60 \div 20 = 3$.
   • Since the cyclist travels 5 miles in one segment, multiply the distance by 3 to find the total distance for the hour: $5 \text{ miles} \times 3 = 15 \text{ miles}$.
   • Therefore, the rate is 15 miles per 1 hour.

2. The Proportion Method:

   • Set up a proportion where $x$ is the unknown distance: $$\frac{5 \text{ miles}}{20 \text{ minutes}} = \frac{x \text{ miles}}{60 \text{ minutes}}$$
   • Cross-multiply: $20x = 300$.
   • Divide by 20: $x = 15$.

Analysis of the Options

• A) (12 miles) / (1 hour): This is incorrect. This might be chosen if a student mistakenly divided 60 by 5, or used an incorrect multiplication factor.
• B) (20 miles) / (1 hour): This is incorrect. A student might choose this by simply taking the "20" from the minutes and moving it to the miles.
• C) (15 miles) / (1 hour): Correct. As calculated above, 20 minutes goes into 60 minutes three times; 5 miles times three equals 15 miles.
• D) (10 miles) / (60 minutes): This is incorrect. This represents doubling the distance without accounting for the fact that 20 minutes fits into 60 minutes three times, not twice.

TEAS Tip: Thinking in Segments

Nursing students often have to calculate IV drip rates or medication dosages over time. Think of an hour as a "pie" cut into slices. If the slice is 20 minutes, there are 3 slices (20, 40, 60). If the slice is 15 minutes, there are 4 slices. If the slice is 30 minutes, there are 2 slices. Just multiply the "per slice" value by the total number of slices to get the hourly rate!