A motorist left Embu for Nairobi, a distance of 240 km, at 8:00 am and traveled at an average speed of 90 km/hr.

Another motorist left Nairobi for Embu at 8:30 am and traveled at 100 km/hr.

Find:

How far did they meet from Nairobi?



Answer :

To begin with, let's identify and break down the information provided:

- Distance between Embu and Nairobi: 240 km
- Speed of the first motorist: 90 km/h
- Speed of the second motorist: 100 km/h
- Departure time of the first motorist: 8:00 AM
- Departure time of the second motorist: 8:30 AM

We want to find out how far they meet from Nairobi.

1. Calculate the time each motorist is traveling before they meet:

Let's denote [tex]\( t \)[/tex] as the time in hours after 8:00 AM when the two motorists meet.

- The first motorist travels at 90 km/h, so in [tex]\( t \)[/tex] hours, the distance covered by the first motorist is [tex]\( 90t \)[/tex] km.
- The second motorist starts at 8:30 AM, so he has been traveling for [tex]\( t - 0.5 \)[/tex] hours when they meet. Therefore, the distance covered by the second motorist is [tex]\( 100(t - 0.5) \)[/tex] km.

2. Set up an equation to represent the total distance:

Since the total distance between Embu and Nairobi is 240 km, we can write the equation:
[tex]\[ 90t + 100(t - 0.5) = 240 \][/tex]

3. Simplify the equation:

[tex]\[ 90t + 100t - 50 = 240 \][/tex]
[tex]\[ 190t - 50 = 240 \][/tex]

4. Solve for [tex]\( t \)[/tex]:

[tex]\[ 190t = 290 \][/tex]
[tex]\[ t = \frac{290}{190} \][/tex]
[tex]\[ t \approx 1.5263 \text{ hours} \][/tex]

So, the two motorists meet approximately 1.5263 hours after the first motorist started his journey at 8:00 AM.

5. Calculate the distance traveled by the second motorist:

Since the second motorist started traveling at 8:30 AM and the two meet 1.5263 hours after 8:00 AM:
[tex]\[ \text{Travel time for the second motorist} = 1.5263 - 0.5 \approx 1.0263 \text{ hours} \][/tex]

The distance covered by the second motorist is given by:
[tex]\[ \text{Distance from Nairobi} = 100 \times 1.0263 = 102.6316 \text{ km} \][/tex]

Conclusion: The two motorists meet approximately 102.63 km from Nairobi.