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Chapter 14: Problem 11

Roberta drove 50 miles in 2 hours. Her rate in miles per hour is equivalent to which of the following proportions? Indicate all such proportions. a. 5 to 20 b. 100 to 4 c. 400 to 16 d. 20 to 500 e. 520 to 20

Short Answer

Expert verified
The proportions equivalent to Roberta's rate are (b) 100 to 4 and (c) 400 to 16.

Step by step solution

01

Identify the rate

In this case, Roberta's rate is 50 miles per 2 hours, which reduces to 25 miles per 1 hour. This is done by dividing 50 by 2.
02

Check each proportion

Now, each given proportion should be checked to see if it reduces to the same rate as Roberta's. Begin by converting each proportion to a rate per hour. a. \( \frac{5}{20} = \frac{1}{4} \) miles per hour b. \( \frac{100}{4} = 25 \) miles per hour c. \( \frac{400}{16} = 25 \) miles per hour d. \( \frac{20}{500} = \frac{1}{25} \) miles per hour e. \( \frac{520}{20} = 26 \) miles per hour
03

Identify the equivalent proportions

b. 100 to 4 and c. 400 to 16 are the only proportions that reduce to a rate of 25 miles per hour. Both of these proportions are equivalent to Roberta's rate per hour. Thus, options b and c are the correct answers.

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