Compute the unit rate. Choose all that are correct.
Understand the Problem
The question is asking to calculate the unit rates based on different mile per hour values given in each option. We need to determine which of the provided options are correct based on the calculations.
Answer
B, C, D
Answer for screen readers
The correct options are B, C, and D.
Steps to Solve
- Calculate Unit Rate for Option A
For option A, we have:
- Distance = $\frac{1}{2}$ mile
- Time = $\frac{1}{4}$ hour
The formula for unit rate (miles per hour) is:
$$ \text{Unit Rate} = \frac{\text{Distance}}{\text{Time}} $$
Calculating:
$$ \text{Unit Rate} = \frac{\frac{1}{2}}{\frac{1}{4}} = \frac{1}{2} \times \frac{4}{1} = 2 \text{ miles per hour} $$
- Calculate Unit Rate for Option B
For option B:
- Distance = $\frac{1}{2}$ mile
- Time = $\frac{1}{8}$ hour
Calculating:
$$ \text{Unit Rate} = \frac{\frac{1}{2}}{\frac{1}{8}} = \frac{1}{2} \times \frac{8}{1} = 4 \text{ miles per hour} $$
- Calculate Unit Rate for Option C
For option C:
- Distance = $\frac{1}{5}$ mile
- Time = $\frac{1}{10}$ hour
Calculating:
$$ \text{Unit Rate} = \frac{\frac{1}{5}}{\frac{1}{10}} = \frac{1}{5} \times \frac{10}{1} = 2 \text{ miles per hour} $$
- Calculate Unit Rate for Option D
For option D:
- Distance = $\frac{1}{2}$ mile
- Time = $\frac{1}{6}$ hour
Calculating:
$$ \text{Unit Rate} = \frac{\frac{1}{2}}{\frac{1}{6}} = \frac{1}{2} \times \frac{6}{1} = 3 \text{ miles per hour} $$
- List All Correct Answers
Now, we compare the calculated unit rates with the options given:
- A = 2 miles per hour
- B = 4 miles per hour (Correct)
- C = 2 miles per hour (Correct)
- D = 3 miles per hour (Correct)
The correct options are B, C, and D.
More Information
The calculations show that options B, C, and D give valid unit rates based on the distance traveled and time taken. Unit rates help to standardize rates for comparison.
Tips
- Confusing the calculation of time and distance.
- Not simplifying fractions properly.
- Incorrectly multiplying or dividing the fractions.
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