Ryan left the science museum and drove
south. Gabriella left three hours later
driving 42 km/h faster in an effort to catch
up to him. After two hours Gabriella finally
caught up. Find Ryan's average speed.

Let's break down the problem step by step.

### Variables and Equations

1. **Let** \( v \) **be Ryan's average speed in km/h**.
2. Gabriella's speed is \( v + 42 \) km/h because she is driving 42 km/h faster than Ryan.
3. Ryan drove for a total time of \( t_R = 3 + 2 = 5 \) hours (since Gabriella started 3 hours later and drove for 2 hours).
4. Gabriella drove for 2 hours.

### Distances

- The distance Ryan traveled can be expressed as:
  \[
  \text{Distance}_{\text{Ryan}} = v \times t_R = v \times 5
  \]
  
- The distance Gabriella traveled can be expressed as:
  \[
  \text{Distance}_{\text{Gabriella}} = (v + 42) \times 2
  \]
  
### Since Gabriella caught up with Ryan, the distances they traveled are equal:

\[
v \times 5 = (v + 42) \times 2
\]

### Solve the Equation

1. Expand the equation:
   \[
   5v = 2v + 84
   \]

2. Subtract \( 2v \) from both sides:
   \[
   3v = 84
   \]

3. Divide by 3:
   \[
   v = 28 \text{ km/h}
   \]

### Conclusion

Ryan's average speed was **28 km/h**.

Would you like more details or have any questions? 

---

Here are 5 related questions you might find interesting:

1. What would be Gabriella's speed if Ryan's speed was 10 km/h faster?
2. How far did Ryan travel before Gabriella caught up?
3. If Gabriella had left 4 hours later instead of 3, what would Ryan's speed be?
4. How long would it take Gabriella to catch up if Ryan was driving at 35 km/h?
5. What if Gabriella drove 10 km/h slower than Ryan, how far would she be after 2 hours?

**Tip:** In problems involving two moving objects, setting up equations based on time and distance is key to finding the solution.

Learn how to find Ryan's average speed using a speed, distance, time problem involving two moving objects. Detailed step-by-step solution provided.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation