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Train and Bus Journey

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?

🚆 Train vs. Bus Journey Use the distance gap and train speed to calculate the missing bus speed! 📋 Known Facts: Time Traveled: 2.5 hours Distance Gap: 75 km Train Speed: 120 km/h CENTRAL STATION 120 km/h ??? km/h 75 km GAP What is the average speed of the bus?

Solution

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)

✅ Solution: Transit Speed Calculation Step-by-step logic combining relative distance and the speed formula. 1️⃣ Calculate the Train's Total Distance We know the train's speed and its travel time. Use Distance = Speed × Time. 120 km/h × 2.5 hours = 300 km TRAIN (300 km) 2️⃣ Calculate the Bus's Total Distance The train is 75 km ahead of the bus, so we subtract the gap from the train's distance. 300 km - 75 km gap = 225 km BUS (225 km) 75 km GAP 3️⃣ Calculate the Bus's Speed We now know the bus's distance and its time. Use Speed = Distance ÷ Time. 225 km ÷ 2.5 hours = 90 km/h AVERAGE BUS SPEED 90 km/h