Anurag travels 45 km in 8 h 45 min (8.75 h) by walking part of the way at 3 km/h and cycling the rest at 8 km/h. How many kilometres did he travel by bicycle?

Introduction / Context:
This is a two-speed mixture problem. Let x be distance cycled at 8 km/h; the remaining (45 − x) km is on foot at 3 km/h. Total time is the sum of segment times.

Given Data / Assumptions:

• Total distance = 45 km.
• Total time = 8.75 h.
• Walking speed = 3 km/h; cycling speed = 8 km/h.

Concept / Approach:
Time equation: x/8 + (45 − x)/3 = 8.75. Solve for x. Since distance and time are positive, the solution must lie between 0 and 45 km.

Step-by-Step Solution:

Verification / Alternative check:
Time = 30/8 + 15/3 = 3.75 + 5 = 8.75 h, matches total.

Why Other Options Are Wrong:
15/20/25 km lead to total times not equal to 8.75 h.

Common Pitfalls:
Mixing time/pace or converting 8 h 45 min incorrectly (8.75 h is exact).

Final Answer:
30 km