The speed ratio of a train to a car is 16 : 15. A bus covers 480 km in 8 h (so its speed is 60 km/h), and the bus speed is 3/4 of the train’s speed. How many kilometres will the car cover in 6 h?

Introduction / Context:
We are given relative speed links among three vehicles. From the bus, we infer the train’s speed, then the car’s speed from the given ratio, and finally compute the distance for the car in 6 hours. Careful chaining avoids unnecessary algebra.

Given Data / Assumptions:

• Bus distance/time = 480 km / 8 h ⇒ bus speed = 60 km/h.
• Bus speed = (3/4) * train speed ⇒ train speed = 60 * (4/3) = 80 km/h.
• Train : Car = 16 : 15 ⇒ car speed = 80 * (15/16) = 75 km/h.

Concept / Approach:
Once car speed is known, distance in 6 hours is straightforward: distance = speed * time.

Step-by-Step Solution:

Verification / Alternative check:
Check proportions: 75 : 80 simplifies to 15 : 16, matching the given ratio.

Why Other Options Are Wrong:
480 km would require 80 km/h; 360 km corresponds to 60 km/h—not the car’s speed.

Common Pitfalls:
Taking 3/4 factor the wrong way (making the train slower than the bus) or mixing up the 16:15 ratio direction.

Final Answer:
450 km