Certainly! Let's solve this problem step-by-step:
1. Understanding the Problem:
- The distance between Akbar's and Birbal's homes is 15 kilometers.
- Akbar walks at a constant speed of 4 kilometers per hour.
- Birbal walks at a constant speed of 6 kilometers per hour.
- We need to determine the time at which they will meet.
2. Combined Speed Calculation:
- When two people are walking towards each other, their combined speed is the sum of their individual speeds.
- Therefore, the combined speed of Akbar and Birbal is [tex]\( 4 \text{ kmph} + 6 \text{ kmph} = 10 \text{ kmph} \)[/tex].
3. Time Calculation:
- The formula to calculate the time taken to cover a certain distance is:
[tex]\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\][/tex]
- Here, the distance to be covered is 15 kilometers, and the combined speed is 10 kilometers per hour.
- Plugging in the values:
[tex]\[
\text{Time} = \frac{15 \text{ km}}{10 \text{ kmph}} = 1.5 \text{ hours}
\][/tex]
4. Converting Time:
- We need to convert 1.5 hours to hours and minutes.
- 1 hour is 60 minutes, so:
[tex]\[
1.5 \text{ hours} = 1 \text{ hour} + (0.5 \times 60 \text{ minutes}) = 1 \text{ hour} + 30 \text{ minutes}
\][/tex]
- Hence, 1.5 hours is equivalent to 1 hour and 30 minutes.
5. Finding the Meeting Time:
- Akbar and Birbal start walking towards each other at 10:00 a.m.
- Adding 1 hour and 30 minutes to their starting time:
[tex]\[
10:00 \text{ a.m.} + 1 \text{ hour} \, 30 \text{ minutes} = 11:30 \text{ a.m.}
\][/tex]
Therefore, Akbar and Birbal will meet at 11:30 a.m.
