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A train and a bus leave the central station at the same time, traveling in the same direction along parallel routes. After 2.5 hours, the train has traveled 75 kilometres more than the bus.
If the average speed of the train is 120 kilometres per hour, what is the average speed of the bus?
Let’s solve this problem step by step:
1. Calculate the distance traveled by the train:
* Time = 2.5 hours
* Speed of train = 120 km/h
* Distance = Speed × Time
* Distance traveled by train = 120 km/h × 2.5 h = 300 km
2. Calculate the distance traveled by the bus:
* The train traveled 75 km more than the bus
* Distance traveled by bus = 300 km – 75 km = 225 km
3. Calculate the speed of the bus:
* We know the distance and time for the bus
* Speed = Distance ÷ Time
* Speed of bus = 225 km ÷ 2.5 h = 90 km/h
Therefore, the average speed of the bus is 90 km/h.
We can verify:
* Train: 120 km/h × 2.5 h = 300 km
* Bus: 90 km/h × 2.5 h = 225 km
* Difference: 300 km – 225 km = 75 km (as stated in the problem)
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