A truck enters a highway driving 60 mph. A car enters the highway at the same place 13 minutes later and drives 74 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 determine the time it will take for the car to catch up to the truck after entering the highway 13 minutes later.

### Step-by-Step Solution

1. **Convert the time difference to hours:**

   The car enters the highway 13 minutes later. Let's convert this time into hours:
   \[
   \text{Time difference in hours} = \frac{13}{60} \text{ hours}
   \]

2. **Calculate the distance the truck has traveled in this time:**

   The truck is driving at 60 mph, so in \(\frac{13}{60}\) hours, it will cover a distance of:
   \[
   \text{Distance traveled by truck} = 60 \times \frac{13}{60} = 13 \text{ miles}
   \]

3. **Set up the equation for the car to catch up:**

   Let \( t \) be the time in hours it takes for the car to catch up to the truck from the moment the car enters the highway.

   The distance the car will travel in time \( t \) is:
   \[
   \text{Distance traveled by car} = 74t
   \]

   The distance the truck will travel in the same time \( t \) is:
   \[
   \text{Distance traveled by truck} = 60t
   \]

   Since the car needs to catch up to the truck, the distance traveled by the car must equal the initial 13 miles plus the distance the truck travels in time \( t \):
   \[
   74t = 60t + 13
   \]

4. **Solve for \( t \):**

   Subtract \( 60t \) from both sides:
   \[
   74t - 60t = 13
   \]
   \[
   14t = 13
   \]
   \[
   t = \frac{13}{14} \text{ hours}
   \]

5. **Convert the time to minutes:**

   To express the time in minutes:
   \[
   t = \frac{13}{14} \times 60 \approx 55.71 \text{ minutes}
   \]

### Conclusion

From the time the car enters the highway, it will take approximately **55.71 minutes** (or **\(\frac{13}{14}\) hours**) for the car to pass the truck.

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Would you like a more detailed explanation, or do you have any further questions?

### Related Questions

1. How far will both the truck and car have traveled by the time they meet?
2. If the car's speed was reduced to 70 mph, how much longer would it take to catch up?
3. What would be the time taken if the car entered 15 minutes later instead of 13 minutes?
4. If the truck increased its speed to 65 mph, how would that change the time for the car to catch up?
5. How would the scenario change if the car had an initial speed delay for the first few miles?

**Tip:** When working with relative speed problems, always consider the time difference in the same unit, usually converting minutes to hours for consistency.


A truck enters a highway driving 60 mph. A car enters the highway at the same place 13 minutes later and drives 74 mph in the same direction. From the time the car enters the highway, how long will it take the car to pass the truck?

Learn how to solve a time-distance problem where a car, entering a highway 13 minutes after a truck, catches up with the truck. The solution involves concepts of relative speed, time, and distance. Suitable for students in Grades 8-10.

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