Juan Martín and Bria are 420 miles apart traveling towards each other. Juan Martín is traveling 20 miles per hour faster than Bria and they meet in 6 hours. How fast was each traveling?

Let's solve the problem step by step.

### Step 1: Define the variables
Let \( v_B \) represent Bria's speed in miles per hour (mph). Then, Juan Martín's speed will be \( v_J = v_B + 20 \) mph because he is traveling 20 mph faster than Bria.

### Step 2: Set up the equation
Since they are traveling towards each other, the sum of the distances they cover in 6 hours will equal the total distance between them, which is 420 miles.

The distance each travels can be represented as:
- Distance traveled by Bria: \( 6v_B \)
- Distance traveled by Juan Martín: \( 6(v_B + 20) \)

So, the equation based on the total distance is:
\[
6v_B + 6(v_B + 20) = 420
\]

### Step 3: Solve the equation
First, expand and simplify the equation:
\[
6v_B + 6v_B + 120 = 420
\]
\[
12v_B + 120 = 420
\]

Next, subtract 120 from both sides:
\[
12v_B = 300
\]

Finally, divide by 12 to solve for \( v_B \):
\[
v_B = 25 \text{ mph}
\]

So, Bria's speed is 25 mph. Now, calculate Juan Martín's speed:
\[
v_J = v_B + 20 = 25 + 20 = 45 \text{ mph}
\]

### Final Answer:
- **Bria was traveling at 25 mph.**
- **Juan Martín was traveling at 45 mph.**

Would you like more details or have any questions about this solution?

Here are five related questions:
1. What would their speeds be if they met after 5 hours instead?
2. How long would it take for them to meet if Bria increased her speed by 10 mph?
3. What if they started 600 miles apart; how would that affect their meeting time?
4. How far would Bria have traveled if they met after 7 hours?
5. If Juan Martín slowed down by 5 mph, how much longer would it take for them to meet?

**Tip:** When solving relative motion problems, always check if the objects are moving towards or away from each other to set up the correct equation.

Explore how to calculate speeds in a relative motion problem involving Juan Martín and Bria, who are 420 miles apart and traveling towards each other. Learn step-by-step how to solve for their speeds using basic speed and distance calculations. Suitable for Grades 9-12.

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