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.