Kali left school and traveled toward her

friend's house at an average speed of 40

km/h. Matt left one hour later and traveled

in the opposite direction with an average

speed of 50 km/h. Find the number of hours

Matt needs to travel before they are 400 km

apart.

Let's break down the problem to find the number of hours Matt needs to travel before they are 400 km apart.

### Variables and Equations

1. **Let** \( t \) **be the time in hours that Matt travels**.
2. Since Kali left one hour earlier, she will have traveled for \( t + 1 \) hours when they are 400 km apart.

### Speeds and Distances

- Kali's speed is 40 km/h, so the distance she travels is:
  \[
  \text{Distance}_{\text{Kali}} = 40 \times (t + 1)
  \]

- Matt's speed is 50 km/h, so the distance he travels is:
  \[
  \text{Distance}_{\text{Matt}} = 50 \times t
  \]

### Total Distance Between Them

Since they are traveling in opposite directions, the total distance between them when they are 400 km apart is the sum of the distances they each traveled:

\[
\text{Distance}_{\text{Kali}} + \text{Distance}_{\text{Matt}} = 400
\]

Substituting the expressions for the distances:

\[
40 \times (t + 1) + 50 \times t = 400
\]

### Solve the Equation

1. Expand the equation:
   \[
   40t + 40 + 50t = 400
   \]

2. Combine like terms:
   \[
   90t + 40 = 400
   \]

3. Subtract 40 from both sides:
   \[
   90t = 360
   \]

4. Divide by 90:
   \[
   t = 4 \text{ hours}
   \]

### Conclusion

Matt needs to travel for **4 hours** before they are 400 km apart.

Would you like more details or have any questions?

---

Here are 5 related questions you might find interesting:

1. How far did Kali travel before they were 400 km apart?
2. If Matt traveled at 60 km/h instead, how long would it take them to be 400 km apart?
3. What would be the distance between them after 3 hours of Matt's travel?
4. If Kali had started 2 hours earlier, how long would Matt need to travel to be 400 km apart?
5. How long would it take for them to be 300 km apart?

**Tip:** In problems involving two objects moving in opposite directions, adding their speeds helps in finding the time it takes for them to be a certain distance apart.

Learn how to calculate the time Matt needs to travel before he and Kali are 400 km apart. This problem involves speed, distance, and time calculations with detailed step-by-step solution and formulas. Suitable for Grades 9-12 students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation