https://file.aiquickdraw.com/mathbot/file/1727664591309ibbu9bjb.jpg

The problem involves two trains, one traveling at 45 km/h and the second at 65 km/h, both leaving the same station but at different times.

### Information:
- **First train**: Departs at 2:00 p.m. and travels at 45 km/h.
- **Second train**: Departs at 4:00 p.m. and travels at 65 km/h.
  
The task is to find when the second train will catch up with the first train.

### Steps:

1. **Time difference**: The first train has a 2-hour head start, since it leaves at 2:00 p.m., and the second leaves at 4:00 p.m.
   
   In that time, the first train will travel:
   \[
   \text{Distance} = \text{Speed} \times \text{Time} = 45 \, \text{km/h} \times 2 \, \text{hours} = 90 \, \text{km}.
   \]

2. **Relative speed**: The second train is faster, so it gains on the first train. The relative speed between the two trains is:
   \[
   \text{Relative speed} = 65 \, \text{km/h} - 45 \, \text{km/h} = 20 \, \text{km/h}.
   \]

3. **Catch-up time**: The second train has to make up the 90 km gap. The time it takes for the second train to catch up is:
   \[
   \text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{90 \, \text{km}}{20 \, \text{km/h}} = 4 \, \text{hours}.
   \]

4. **Catch-up time of day**: The second train left at 4:00 p.m., and it will take 4 hours to catch up, so the catch-up time is:
   \[
   4:00 \, \text{p.m.} + 4 \, \text{hours} = 8:00 \, \text{p.m.}.
   \]

### Answer:
The second train will catch up with the first train at **8:00 p.m.**.

---

Would you like more details or have any other questions?

Here are 5 related questions you might find interesting:
1. How far will both trains have traveled by 8:00 p.m.?
2. What if the first train had traveled at 50 km/h instead of 45 km/h?
3. How would the solution change if the second train left at 3:00 p.m.?
4. Can you determine the distance between the two trains at any time before 8:00 p.m.?
5. How much earlier would the second train catch up if it traveled at 70 km/h?

**Tip**: In "catch-up" problems, identifying the relative speed between the two objects is crucial to determining when one will catch the other.

A train left a station at 2:00 p.m. and traveled 45 km/hr. A second train left the station at 4:00 p.m. and traveled 65 km/hr in the same direction. At what time will the second train catch the first?

Solve the problem of two trains leaving a station at different times and speeds. Learn how to calculate when the second train will catch up with the first using speed, distance, and time formulas. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation