Complete the table.

A jogger and cyclist started at the same point and traveled for 3 hours in opposite directions until they were 66 miles apart. The cyclist traveled 11 mph faster than the jogger.

Rate · Time = DistanceRateTimeDistance

Jogger

*x*

3

 *x*

Cyclist

*y*

3

 *y*

Total

Write a system of two equations that can be used to find *x* and *y*. DO NOT SOLVE THE SYSTEM.

 
 *x* +  *y* = 66

*y* = *x* + 

We are given that the jogger and cyclist traveled in opposite directions for 3 hours and were 66 miles apart. The cyclist's speed is 11 mph faster than the jogger's speed.

Let:
- \( x \) be the jogger's speed in mph,
- \( y \) be the cyclist's speed in mph.

From the information given, we can create two equations:

1. The total distance covered by both the jogger and cyclist in 3 hours is 66 miles. Since distance = rate × time, the distance the jogger covers is \( 3x \), and the distance the cyclist covers is \( 3y \). Therefore, the first equation is:
   \[
   3x + 3y = 66
   \]
   Simplifying, we get:
   \[
   x + y = 22
   \]

2. We are also told that the cyclist’s speed is 11 mph faster than the jogger’s speed. So, the second equation is:
   \[
   y = x + 11
   \]

Thus, the system of equations is:
\[
x + y = 22
\]
\[
y = x + 11
\]

This is the system of equations that can be used to find \( x \) (the jogger's speed) and \( y \) (the cyclist's speed).

Would you like any additional details or have further questions?

Here are five related questions for deeper understanding:
1. How do we solve the system of equations for \( x \) and \( y \)?
2. What would happen if the cyclist's speed were 5 mph faster than the jogger's speed?
3. Can we generalize this problem to any time duration other than 3 hours?
4. How would the system change if the cyclist and jogger traveled in the same direction?
5. What is the physical interpretation of each term in the equation?

**Tip:** Always check if a system of equations can be simplified before solving—this often makes solving easier.

A jogger and cyclist started at the same point and traveled for 3 hours in opposite directions until they were 66 miles apart. The cyclist traveled 11 mph faster than the jogger. Write a system of two equations that can be used to find the jogger's speed (x) and the cyclist's speed (y). DO NOT SOLVE THE SYSTEM.

Learn how to set up a system of equations to solve a jogger and cyclist problem. The problem involves a jogger and cyclist traveling for 3 hours in opposite directions with the cyclist moving 11 mph faster. Suitable for Grades 8-10, this problem covers algebraic concepts like setting up and solving systems of linear equations.

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