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

1414 

minutes later and drives 

6868 

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

Let's solve this problem step by step.

### Given:
- The truck is traveling at 60 mph.
- The car enters the highway 14 minutes later and is traveling at 68 mph.
- We need to find how long it will take for the car to pass the truck from the moment the car enters the highway.

### Step 1: Convert 14 minutes into hours
Since the speeds are given in miles per hour, we need to convert 14 minutes into hours:
\[
14 \text{ minutes} = \frac{14}{60} \text{ hours} = \frac{7}{30} \text{ hours}.
\]

### Step 2: Find the head start of the truck
In \(\frac{7}{30}\) hours, the truck will have traveled:
\[
\text{Distance covered by the truck} = 60 \times \frac{7}{30} = 14 \text{ miles}.
\]
So, the truck has a 14-mile head start when the car enters the highway.

### Step 3: Set up the equation to find the time
From the time the car enters the highway, it needs to cover the 14-mile head start at a relative speed. The car is traveling at 68 mph, and the truck is traveling at 60 mph. The relative speed between the car and the truck is:
\[
\text{Relative speed} = 68 - 60 = 8 \text{ mph}.
\]
Now, the car needs to cover 14 miles at a speed of 8 mph. The time it will take for the car to pass the truck is:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{14}{8} = 1.75 \text{ hours}.
\]

### Answer:
It will take the car **1.75 hours** (or 1 hour and 45 minutes) to pass the truck from the moment it enters the highway.

Would you like more details or have any questions?

### Related Questions:
1. How do you solve problems involving relative speeds?
2. How can you convert between different time units efficiently?
3. What is the importance of relative speed in motion problems?
4. How can you verify your solution by checking

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?

Find out how to calculate the time it takes for a car driving at 68 mph to pass a truck driving at 60 mph on a highway. This problem involves understanding relative speed and applying distance, speed, and time formulas. Suitable for middle school students (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