A truck enters a highway driving 60 mph. A car enters the highway at the same place 6 minutes later and drives 70 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?

To solve this problem, we need to find out how long it will take for the car to catch up to the truck. Here's how we can approach it:

### Step 1: Distance traveled by the truck in 6 minutes
The truck enters the highway 6 minutes (or \( \frac{6}{60} = 0.1 \) hours) before the car. The truck is traveling at 60 miles per hour, so the distance it covers in that time is:
\[
\text{Distance by truck} = 60 \times 0.1 = 6 \text{ miles}
\]
So, when the car enters the highway, the truck is 6 miles ahead.

### Step 2: Relative speed between the car and the truck
The car is traveling at 70 miles per hour, and the truck is traveling at 60 miles per hour. Therefore, the car is gaining on the truck at a rate of:
\[
\text{Relative speed} = 70 - 60 = 10 \text{ miles per hour}
\]

### Step 3: Time for the car to catch up
The car needs to close the 6-mile gap at a rate of 10 miles per hour. The time it will take for the car to catch up is:
\[
\text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{6}{10} = 0.6 \text{ hours}
\]
This is equivalent to:
\[
0.6 \times 60 = 36 \text{ minutes}
\]

### Conclusion:
It will take the car 36 minutes to pass the truck from the time the car enters the highway.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What if the car's speed were 80 mph instead of 70 mph? How long would it take then?
2. How far will the truck have traveled by the time the car passes it?
3. If the car entered the highway 10 minutes later instead of 6, how would that affect the time to catch up?
4. How far would the car have traveled by the time it catches up to the truck?
5. What if both vehicles started at the same time, but with the same speeds as given? How long would it take for the car to overtake the truck?

**Tip:** When dealing with relative motion problems, always focus on the difference in speeds and the distance between the two objects.

In this example, a car overtakes a truck on the highway. Learn how to calculate the time it takes for the car to catch up to the truck by using relative motion concepts, speed, and time formulas. Perfect for students in Grades 6-8 looking to master relative speed problems.

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