A train covers 240 km in 12 hours, so its average speed is 20 km/h. A bus travels at three fourths of this train speed. How many kilometres will the bus cover in 7 hours at that speed?

Introduction / Context:This problem compares average speeds of two vehicles using a fixed ratio and asks for the distance covered in a given time. It tests proportional reasoning using the distance formula distance = speed * time.

Given Data / Assumptions:

• Train covers 240 km in 12 h.
• Bus speed is three fourths of train speed.
• We need bus distance in 7 h.

Concept / Approach:Compute train speed, scale it by 3/4 to get bus speed, then multiply by time to get distance. Keep units consistent in km and hours.

Step-by-Step Solution:

Verification / Alternative check:Proportionally, in 4 h the train would do 80 km; the bus would do 60 km. In 7 h the bus adds 45 km more, totaling 105 km, which is consistent.

Why Other Options Are Wrong:100 km, 110 km, and 115 km correspond to speeds of about 14.29, 15.71, and 16.43 km/h respectively, which do not equal 15 km/h (three fourths of 20 km/h).

Common Pitfalls:Confusing the 3/4 factor to apply on distance instead of speed, and mixing time units.

Final Answer:105 km