Relative speeds chained (A twice B, B thrice C) A is twice as fast as B, and B is thrice as fast as C. If C covers a journey in 42 minutes, how long will A take for the same journey?

Introduction / Context:Composite speed relations can be chained by multiplication. If A is 2 times B and B is 3 times C, then A is 6 times C. Time for the same distance scales inversely with speed.

Given Data / Assumptions:

• A = 2B; B = 3C ⇒ A = 6C (in speed).
• Time(C) = 42 min.

Concept / Approach:Time(A) = Time(C) / (A/C) since time ∝ 1/speed.

Step-by-Step Solution:

Verification / Alternative check:If C's speed is 1 unit, A's is 6 units; for a fixed distance, time scales reciprocally.

Why Other Options Are Wrong:14 and 28 are larger than the reciprocal factor implies; 63 min would be slower than C.

Common Pitfalls:Adding factors (2 + 3) instead of multiplying (2 * 3) for chained relations.

Final Answer:7 min