A train is traveling from City A to City B at an average speed of 60 miles per hour. At the same time, a car is traveling from City B to City A at an average speed of 40 miles per hour. If the distance between the two cities is 240 miles, and the train and car pass each other at a point somewhere between the two cities, how long will it take for the train to reach City B after they pass each other?

To solve this problem, let's break it down into steps.

### Step 1: Calculate the time it takes for the train and car to meet.
The distance between City A and City B is 240 miles. The train and car are traveling towards each other, so their relative speed is the sum of their individual speeds:

\[
\text{Relative speed} = 60 \, \text{miles per hour (train)} + 40 \, \text{miles per hour (car)} = 100 \, \text{miles per hour}
\]

Now, we calculate the time it takes for them to meet:

\[
\text{Time to meet} = \frac{\text{Distance between the cities}}{\text{Relative speed}} = \frac{240 \, \text{miles}}{100 \, \text{miles per hour}} = 2.4 \, \text{hours}
\]

### Step 2: Determine the distance the train travels before meeting the car.
In 2.4 hours, the train travels:

\[
\text{Distance traveled by the train} = \text{Speed of the train} \times \text{Time to meet} = 60 \, \text{miles per hour} \times 2.4 \, \text{hours} = 144 \, \text{miles}
\]

### Step 3: Calculate the remaining distance the train has to travel after they pass each other.
Since the distance between City A and City B is 240 miles and the train has already traveled 144 miles, the remaining distance to City B is:

\[
\text{Remaining distance} = 240 \, \text{miles} - 144 \, \text{miles} = 96 \, \text{miles}
\]

### Step 4: Calculate the time it takes for the train to reach City B after they pass each other.
The time it will take for the train to cover the remaining 96 miles at a speed of 60 miles per hour is:

\[
\text{Time to reach City B} = \frac{\text{Remaining distance}}{\text{Speed of the train}} = \frac{96 \, \text{miles}}{60 \, \text{miles per hour}} = 1.6 \, \text{hours}
\]

So, it will take the train **1.6 hours** to reach City B after they pass each other.

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Would you like more details or have any questions? Here are 5 related questions you might find interesting:

1. What would happen if the car's speed increased to 50 miles per hour?
2. How far from City A will the train and car meet?
3. If the train had started 30 minutes later, when and where would they meet?
4. What if both the car and the train had started at the same time from the same city but in opposite directions?
5. How would the situation change if the distance between City A and City B was doubled?

**Tip:** When dealing with problems involving relative speeds, always sum the speeds when objects are moving towards each other and subtract them when they are moving in the same direction.

Learn how to calculate the time it takes for a train to reach City B after passing a car traveling in the opposite direction. This problem involves concepts of relative speed, distance, and time, suitable for students in Grades 6-8.

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