two cars leave traveling in opposite directions. once car travels 60 mph and the other 64 mph how long until they are 310 miles apart

To solve the problem, we can use the concept of relative speed. Since the two cars are traveling in opposite directions, we add their speeds together to find their relative speed.

### Step 1: Determine the relative speed.
- Speed of the first car = 60 mph
- Speed of the second car = 64 mph

Relative speed = \( 60 \, \text{mph} + 64 \, \text{mph} = 124 \, \text{mph} \)

### Step 2: Use the formula to find time.
The formula for time when distance and speed are known is:

\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]

Here, the distance is 310 miles, and the relative speed is 124 mph.

\[
\text{Time} = \frac{310 \, \text{miles}}{124 \, \text{mph}} \approx 2.5 \, \text{hours}
\]

So, it will take approximately 2.5 hours for the two cars to be 310 miles apart.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. What if one of the cars increased its speed by 10 mph? How would the time change?
2. How far apart would the cars be after 1 hour of travel?
3. What if the cars were initially 20 miles apart? How would that affect the time?
4. If both cars reduced their speeds by 5 mph, how long would it take to be 310 miles apart?
5. What if the cars traveled for 4 hours? How far apart would they be?

**Tip:** When solving relative motion problems, always consider whether the objects are moving towards or away from each other, as this determines whether to add or subtract their speeds.

Two cars leave traveling in opposite directions. One car travels 60 mph and the other 64 mph. How long until they are 310 miles apart?

Learn how to calculate the time it takes for two cars traveling in opposite directions at speeds of 60 mph and 64 mph to be 310 miles apart. This problem covers the concept of relative speed and the formula for calculating time when distance and speed are known. Suitable for students in Grades 6-8.

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