A bus leaves Kisumu at 9:30 am traveling at 81 km/hr. A matatu leaves Nairobi at 10:10 am traveling at 100 km/hr. How long will it take the matatu to catch up to the bus?

Step 1: Calculate the head start distance of the bus.
The bus left Kisumu at 9:30 am. The matatu left Nairobi at 10:10 am.
The time difference (head start for the bus) is $10:10 \text{ am} - 9:30 \text{ am} = 40 \text{ minutes}$.
Convert 40 minutes to hours:

$$T_{headstart} = \frac{40}{60} = \frac{2}{3} \text{ hours}$$

The speed of the bus is $V_B = 81 \text{ km/hr}$.
The distance covered by the bus during its head start is:

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