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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 in miles per hour are b. 100 to 4 and c. 400 to 16.

Step by step solution

01

Calculate Roberta's speed

Roberta's speed can be calculated by dividing the total distance she drove by the total time taken. In this case, it would be \( \frac{50 miles}{2 hours} = 25 miles/hour \)
02

Compare with the given proportions

This step involves comparing Roberta's speed with each of the given proportions. A proportion is equivalent to Roberta's speed if its ratio is equal to \(25 miles/hour\). To find this, divide the first number of the proportion by the second number.
03

Check proportion a. 5 to 20

Checking the first proportion \( a. \frac{5}{20}= 0.25 \) which is not equal to 25 miles/hour.
04

Check proportion b. 100 to 4

Checking the second proportion \( b. \frac{100}{4}= 25 \), which is equal to 25 miles/hour. So, b is one of the solutions.
05

Check proportion c. 400 to 16

Checking third proportion \( c. \frac{400}{16}= 25 \), which is equal to 25 miles/hour. So, c is also one of the solutions.
06

Check proportion d. 20 to 500

Checking fourth proportion \( d. \frac{20}{500}= 0.04 \), which is not equal to 25 miles/hour.
07

Check proportion e. 520 to 20

Checking fifth proportion \( e. \frac{520}{20}= 26 \), which is not equal to 25 miles/hour.

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