Zara and Steven both track the number of miles they bike each week. Zara was already biking 60 miles per week, and started biking 20 more miles each week. Steven was already biking 90 miles per week, and started biking 10 more miles each week. Is there a time when they bike the same number of miles each week?

Question

The relationships between x, the number of weeks, and y, the number of miles Zara and Steven bike each week, are graphed on the coordinate plane below. What is the point of intersection?
Zara
Steven
0
1
2
3
4
5
6
7
8
9
10
0
20
40
60
80
100
120
140
160
180
200
Time (weeks)
Number of miles
The point of intersection is (
,

Answer 1

To find the point of intersection where Zara and Steven bike the same number of miles each week, we need to establish equations for their biking.

1. Zara's Miles:

   • Starting miles: 60
   • Additional miles per week: 20
   • Therefore, after \( x \) weeks, Zara's total miles can be represented by the equation: \[ y = 60 + 20x \]

2. Steven's Miles:

   • Starting miles: 90
   • Additional miles per week: 10
   • Therefore, after \( x \) weeks, Steven's total miles can be represented by the equation: \[ y = 90 + 10x \]

Now, to find the intersection point where they bike the same number of miles, we set the equations equal to each other:

\[ 60 + 20x = 90 + 10x \]

Next, we'll solve for \( x \):

1. Subtract \( 10x \) from both sides: \[ 60 + 10x = 90 \]

2. Subtract 60 from both sides: \[ 10x = 30 \]

3. Divide by 10: \[ x = 3 \]

Now that we have \( x \), we can substitute it back into either equation to find \( y \):

Using Zara's equation: \[ y = 60 + 20(3) = 60 + 60 = 120 \]

So the point of intersection, where they both bike the same number of miles each week, is:

\[ \text{Point of intersection is } (3, 120) \]

Thus, the final answer is: \[ \text{The point of intersection is } (3, 120). \]