The problem presents a graph showing the distance from school versus time for two girls, Feng and Wei, who are riding bikes. We are asked to: a. Write an equation for each girl's line. b. Determine how fast each girl is riding (their speeds). c. Find when Feng and Wei meet and how far they are from school at that point.

1. Problem Description

The problem presents a graph showing the distance from school versus time for two girls, Feng and Wei, who are riding bikes. We are asked to:

a. Write an equation for each girl's line.

b. Determine how fast each girl is riding (their speeds).

c. Find when Feng and Wei meet and how far they are from school at that point.

2. Solution Steps

a. Equations of the lines:

We need to find the slope ($m$) and y-intercept ($b$) for each line to write the equation in the form $y = mx + b$.

For Feng's line:

Two points on Feng's line are approximately $(0, 0)$ and $(8, 32)$.

The slope $m_{Feng} = \frac{32 - 0}{8 - 0} = \frac{32}{8} = 4$.

The y-intercept $b_{Feng}$ is

0. So, Feng's equation is $y = 4x$.

For Wei's line:

Two points on Wei's line are approximately $(0, -8)$ and $(8, 32)$.

The slope $m_{Wei} = \frac{32 - (-8)}{8 - 0} = \frac{40}{8} = 5$.

The y-intercept $b_{Wei}$ is -

8. So, Wei's equation is $y = 5x - 8$.

b. Speeds of the girls:

The speed is the absolute value of the slope of the line since the slope represents the rate of change of distance with respect to time.

Feng's speed: $4$ miles per hour.

Wei's speed: $5$ miles per hour.

c. When and where they meet:

To find the meeting point, we set the two equations equal to each other:

$4x = 5x - 8$

$8 = 5x - 4x$

$x = 8$

So, they meet at $x = 8$ hours.

To find the distance from school at that point, we substitute $x = 8$ into either equation. Using Feng's equation:

$y = 4(8) = 32$

So, they meet 32 miles from school.

3. Final Answer

a. Feng's equation: $y = 4x$. Wei's equation: $y = 5x - 8$.

b. Feng's speed: 4 miles per hour. Wei's speed: 5 miles per hour.

c. They meet after 8 hours, and they are 32 miles from school.