A bus left Busia at 9:00 am at a speed of 80 km/h. A car left Nairobi at 8:30 am at a speed of 120 km/h. The…

Question

A bus left Busia at 9:00 am at a speed of 80 km/h. A car left Nairobi at 8:30 am at a speed of 120 km/h. The distance between Nairobi and Busia is 400 km. Calculate the time the two vehicles meet.

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Here's the solution to the problem, based on the information deciphered from the image and the context of the previous question.

Problem Statement (Deciphered from image):
A bus left Busia at 9:00 am at a speed of 80 km/h. A car left Nairobi at 8:30 am at a speed of 120 km/h. The distance between Nairobi and Busia is 400 km.

b) The time the two vehicles meet

Calculate the distance covered by the car before the bus starts.
The car leaves Nairobi at 8:30 am, and the bus leaves Busia at 9:00 am. This means the car travels for 30 minutes (0.5 hours) alone.
$\text{Distance covered by car} = \text{Speed of car} \times \text{Time}$ $\text{Distance covered by car} = 120 \text{ km/h} \times 0.5 \text{ h} = 60 \text{ km}$
Calculate the remaining distance between the car and the bus at 9:00 am.
The total distance between Nairobi and Busia is 400 km.
$\text{Remaining distance} = \text{Total distance} - \text{Distance covered by car}$ $\text{Remaining distance} = 400 \text{ km} - 60 \text{ km} = 340 \text{ km}$
Calculate the relative speed of the two vehicles.
Since they are moving towards each other, their speeds add up.
$\text{Relative speed} = \text{Speed of car} + \text{Speed of bus}$ $\text{Relative speed} = 120 \text{ km/h} + 80 \text{ km/h} = 200 \text{ km/h}$
Calculate the time taken for them to meet after 9:00 am.
$\text{Time to meet} = \frac{\text{Remaining distance}}{\text{Relative speed}}$ $\text{Time to meet} = \frac{340 \text{ km}}{200 \text{ km/h}} = \frac{34}{20} \text{ hours} = \frac{17}{10} \text{ hours} = 1.7 \text{ hours}$
Convert

A bus left Busia at 9:00 am at a speed of 80 km/h. A car left Nairobi at 8:30 am at a speed of 120 km/h. The distance between Nairobi and Busia is 400 km. Calculate the time the two vehicles meet.

Step-by-step solution

Calculate the distance covered by the car before the bus starts.

Calculate the remaining distance between the car and the bus at 9:00 am.

Calculate the relative speed of the two vehicles.

Calculate the time taken for them to meet after 9:00 am.

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