A truck enters a highway driving 60 mph. A car enters the highway at the same place

14

minutes later and drives

68

mph in the same direction. From the time the car enters the​ highway, how long will it take the car to pass the​ truck


We can solve this problem using the concept of relative motion.

### Step 1: Define variables
- The truck's speed is \( 60 \, \text{mph} \).
- The car's speed is \( 68 \, \text{mph} \).
- The truck has a 14-minute head start, which is equivalent to \( \frac{14}{60} = \frac{7}{30} \, \text{hours} \).

### Step 2: Distance the truck has traveled in 14 minutes
In \( \frac{7}{30} \, \text{hours} \), the truck has already traveled:
\[
\text{Distance by truck} = 60 \times \frac{7}{30} = 14 \, \text{miles}.
\]
So, when the car enters the highway, the truck is 14 miles ahead.

### Step 3: Relative speed
The car is moving faster than the truck. The relative speed between the car and the truck is:
\[
\text{Relative speed} = 68 - 60 = 8 \, \text{mph}.
\]

### Step 4: Time for the car to catch up
To catch up with the truck, the car needs to close the 14-mile gap at a relative speed of 8 mph. The time it takes to close this gap is:
\[
\text{Time} = \frac{\text{Distance}}{\text{Relative speed}} = \frac{14}{8} = 1.75 \, \text{hours}.
\]

So, it will take the car **1.75 hours** (or 1 hour and 45 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:
1. What if the truck's speed was increased to 65 mph? How would that affect the time?
2. How far will the car have traveled when it catches up to the truck?
3. What if the car entered the highway 20 minutes later instead of 14?
4. How much distance does the car gain per minute relative to the truck?
5. Can you calculate the time taken if both vehicles were accelerating at different rates?

**Tip:** Always convert minutes into hours when dealing with speed in miles per hour (mph) for consistent units in time calculations.

A truck enters a highway driving 60 mph. A car enters the highway at the same place 14 minutes later and drives 68 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 calculate the time it will take for a car driving at 68 mph to pass a truck driving at 60 mph, with the truck having a 14-minute head start. This problem covers key concepts of relative motion, speed, distance, and time, and includes step-by-step solutions. Suitable for students in Grades 8-10.

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