Given data:
Total distance of the trip is 555 kilometres.
Speed of the bus is 60 kilometres per hour.
Speed of the car is 75 kilometres per hour.
Total time taken is 8 hours.
Let, the total distance covered by the bus x kilometres (assume x as a variable to calculate the total distance covered by the bus)
So, the total distance covered by the car
= Total distance - distance covered by the bus
= (555 - x) km
Now,
The bus covers 60 km in = 1 hour
The bus covers 1 km in = \(\frac 1{60}\) hour
The bus covers x km in = \(\frac x{60}\) hours
And,
The car covers 75 km in = 1 hour
The car covers 1 km in = \(\frac1{75}\) hour
The car covers 555 - x km in = \(\frac{555 - x}{75}\) hours
So, the total time of the journey
\(= \frac x{60} +\frac{555 - x}{75}\) hours
Now, if we compare the total time of the journey that we calculated and the total time of the journey given in the question, then we will get the following equation
\(\frac x{60} + \frac {555-x}{75} = 8\)
\(\frac {5x + 2220-4x}{300} = 8\)
\(x + 2220 = 2400\)
\(x = 180\)
So, the bus travelled a distance of 180 kilometres.
