To solve this problem, we need to determine the point where the bus and the matatu meet. Both vehicles travel towards each other starting at the same time, but the matatu has a 45-minute (or 0.75 hours) stop along the way. Let's denote the following:
- Distance between the towns, \( D = 220 \) km
- Speed of the bus, \( S_b = 60 \) km/h
- Speed of the matatu, \( S_m = 80 \) km/h
- Let \( T \) be the time in hours for the bus and matatu to meet.
Since the matatu stopped for 0.75 hours, it effectively travels for \( T - 0.75 \) hours.
First, let's express the distances each vehicle travels in terms of \( T \):
- Distance covered by the bus, \( D_b \):
\[ D_b = S_b \times T = 60 \, \text{km/h} \times T \]
- Distance covered by the matatu, \( D_m \):
\[ D_m = S_m \times (T - 0.75) = 80 \, \text{km/h} \times (T - 0.75) \]
Because they meet, the sum of the distances \( D_b \) and \( D_m \) is equal to the total distance \( D \):
\[ D_b + D_m = 220 \, \text{km} \]
Substitute the expressions for \( D_b \) and \( D_m \):
\[ 60T + 80(T - 0.75) = 220 \]
Simplify the equation:
\[ 60T + 80T - 60 = 220 \]
\[ 140T - 60 = 220 \]
\[ 140T = 280 \]
\[ T = 2 \, \text{hours} \]
Now, we need to calculate the distance covered by the bus before meeting the matatu:
\[ D_b = S_b \times T = 60 \, \text{km/h} \times 2 \, \text{hours} = 120 \, \text{km} \]
Therefore, the distance covered by the bus before meeting the matatu is \( 120 \) kilometers.