Two trucks leave a warehouse at the same time.  One travels due north at an average speed of 5858 miles per hour, and the other travels due south at an average speed of 6464 miles per hour.  After how many hours will the two trucks be 427427 miles apart?

To solve the problem, we need to determine how many hours it will take for the two trucks to be 427,427 miles apart. 

### Step 1: Understand the problem
- **Truck 1** is traveling due north at 5,858 miles per hour.
- **Truck 2** is traveling due south at 6,464 miles per hour.
- The trucks are moving in opposite directions, so their distances add up over time.

### Step 2: Find the relative speed
Since the trucks are moving in opposite directions, their relative speed is the sum of their individual speeds:
\[
\text{Relative Speed} = 5858 \text{ miles per hour} + 6464 \text{ miles per hour} = 12,322 \text{ miles per hour}
\]

### Step 3: Use the formula for distance
The formula for distance is:
\[
\text{Distance} = \text{Speed} \times \text{Time}
\]
We want to find the time \( t \) when the distance between the trucks is 427,427 miles:
\[
427,427 \text{ miles} = 12,322 \text{ miles per hour} \times t
\]

### Step 4: Solve for time \( t \)
To solve for \( t \), divide both sides of the equation by the relative speed:
\[
t = \frac{427,427 \text{ miles}}{12,322 \text{ miles per hour}}
\]
\[
t \approx 34.68 \text{ hours}
\]

### Final Answer:
The two trucks will be 427,427 miles apart after approximately **34.68 hours**.

Would you like more details or have any questions? Here are some related problems:

1. Two cars are 600 miles apart and moving towards each other. If Car A travels at 60 mph and Car B at 75 mph, how long will it take for them to meet?
2. Two planes leave an airport at the same time, one flying east at 500 mph and the other flying west at 450 mph. How far apart will they be after 3 hours?
3. A cyclist travels north at 15 mph, and another cyclist travels south at 12 mph. How long will it take for them to be 81 miles apart?
4. A boat sails upstream at 20 mph and another downstream at 30 mph. If they started together, how far apart will they be after 2 hours?
5. Two runners start from the same point and run in opposite directions. If Runner A runs at 8 mph and Runner B at 6 mph, how far apart will they be after 5 hours?

**Tip:** When two objects move in opposite directions, their speeds add up when calculating the distance between them.

Learn how to calculate the distance between two trucks traveling in opposite directions, one northbound at 5858 miles per hour and the other southbound at 6464 miles per hour. Follow a step-by-step solution to find out how long it will take for them to be 427,427 miles apart.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation