A bus travels at 90 km/h. A car leaves 2 hours and 20 minutes after the bus, traveling at 110 km/h. The total distance between their starting points is 760 km. When do they meet?

Here's the solution to question 23:

a)

i) The time of the day the two vehicles met:

Step 1: Calculate the head start time for the bus.
The bus leaves at 0815 hours. The car leaves at 1035 hours.

$$\text{Head start time} = 1035 - 0815 = 2 \text{ hours } 20 \text{ minutes}$$

Convert minutes to hours: $20 \text{ minutes} = \frac{20}{60} \text{ hours} = \frac{1}{3} \text{ hours}$.

$$\text{Head start time} = 2 + \frac{1}{3} \text{ hours} = \frac{7}{3} \text{ hours}$$

Step 2: Calculate the distance covered by the bus during its head start.

$$\text{Distance covered by bus} = \text{Speed of bus} \times \text{Head start time}$$ $$\text{Distance covered by bus} = 90 \text{ km/h} \times \frac{7}{3} \text{ hours} = 210 \text{ km}$$

Step 3: Calculate the remaining distance when the car starts.

$$\text{Remaining distance} = \text{Total distance} - \text{Distance covered by bus}$$ $$\text{Remaining distance} = 760 \text{ km} - 210 \text{ km} = 550 \text{ km}$$

Step 4: Calculate the relative speed of the two vehicles.
Since they are moving towards each other, their speeds add up.

$$\text{Relative speed} = \text{Speed of bus} + \text{Speed of car}$$ $$\text{Relative speed} = 90 \text{ km/h} + 110 \text{ km/h} = 200 \text{ km/h}$$

Step 5: Calculate the time taken for them to meet after the car starts.

$$\text{Time to meet} = \frac{\text{Remaining distance}}{\text{Relative speed}}$$ $$\text{Time to meet} = \frac{550 \text{ km}}{200 \text{ km/h}} = \frac{11}{4} \text{ hours}$$

Convert this time to hours and minutes:

$$$$