The average rate of the first part of Yi’s walk on a park loop was 4 miles per hour. She then met up with a friend and the two walked the rest of the way at an average rate of 5 miles per hour. The entire 3-mile walk took Yi 42 minutes (0.7 hour). Which equation can be used to solve for x, the time in hours that Yi spent walking before meeting her friend?

Question

A table showing Rate in mile per hour, Time in hours, and Distance in miles. The first row shows Part 1 and has 4, x, and 4 x. The second row shows Part 2, and has, 5, 0.7 minus x, and 5 left-parenthesis 0.7 minus x right-parenthesis.

A. x = 0.7 – x
B. x + (0.7 – x) = 1
C. 4x + 5(0.7 – x) = 1
D. 4x + 5(0.7 – x) = 3

Answer 1

To solve for \( x \), the time in hours that Yi spent walking before meeting her friend, we can analyze the given information.

1. Part 1: The average speed for the first part of Yi's walk is 4 miles per hour. If she spent \( x \) hours walking before meeting her friend, the distance covered in this part is calculated as: \[ \text{Distance}_1 = \text{Rate} \times \text{Time} = 4x \text{ miles} \]

2. Part 2: After meeting her friend, they walked together at an average speed of 5 miles per hour for the remaining time, which is \( 0.7 - x \) hours. The distance covered in this part is: \[ \text{Distance}_2 = \text{Rate} \times \text{Time} = 5(0.7 - x) \text{ miles} \]

3. Total Distance: The total distance of the entire walk is 3 miles. Therefore, we can set up the equation: \[ \text{Distance}_1 + \text{Distance}_2 = 3 \] Substituting our expressions for distances, we have: \[ 4x + 5(0.7 - x) = 3 \]

This equation reflects the total distance walked in terms of the time \( x \).

Therefore, the correct answer is:

D. \( 4x + 5(0.7 - x) = 3 \)