Two brothers leave from the same point driving in opposite​ directions, the first brother driving at 

6565 

miles per hour and the second at 

5555 

mph. The first brother has a​ one-hour head start. If each brother has a communication device that allows him to talk to the other for up to a 

300300​-mile 

​range, how long will they be able to talk to each​ other?

Question content area bottom

Part 1

The communication devices will be out of range 

2.962.96 

hours after the first brother left.

​(Simplify your answer. Type an​ integer, fraction, or mixed​ number.) 

Given the problem, we already calculated that the brothers will be able to talk for **2.96 hours** after the first brother left.

To express this time in a simplified form:

### Step 1: Convert 2.96 hours into a more precise form.
- \( 2.96 \) can be written as \( 2 + 0.96 \) hours.

### Step 2: Simplify \( 0.96 \) as a fraction.
- \( 0.96 \) is equivalent to \( \frac{96}{100} \), which simplifies to \( \frac{24}{25} \).

### Step 3: Write the total time as a mixed number.
- Combining the integer part and the fractional part:
  \[
  2.96 \text{ hours} = 2 \frac{24}{25} \text{ hours}
  \]

### Final Answer:
The communication devices will be out of range **2 \(\frac{24}{25}\)** hours after the first brother left.

Would you like to explore this further or have any questions?

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**Related Questions:**
1. How long would they be able to communicate if the first brother drove at 60 mph instead of 65 mph?
2. What would be the range if the brothers could talk for 4 hours?
3. What distance would the brothers cover together in the time they are in communication?
4. How far apart are they after 3 hours if they continue driving?
5. What if the communication range was extended to 350 miles?

**Tip:** When simplifying decimals into fractions, consider using the least common denominator to reduce the fraction to its simplest form.

Explore how long two brothers, driving in opposite directions at different speeds, can communicate using devices with a 300-mile range. Understand the calculation involved when one brother has a one-hour head start. Suitable for students in Grades 7-9.

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