Proportional Speeds – Time scaling across linked speeds: A is twice as fast as B, and B is three times as fast as C. If C covers a certain distance in 56 minutes, how long will A take to cover the same distance?

Introduction / Context:
The times taken to cover the same distance are inversely proportional to speeds. Given chained speed relations among A, B, and C, we can express A as a multiple of C and scale the time accordingly.

Given Data / Assumptions:

• A = 2B and B = 3C ⇒ A = 6C.
• Time for C to cover the distance = 56 min.
• Distance is the same for all individuals.

Concept / Approach:
With A = 6C in speed terms, time scales inversely, so T_A = T_C / 6. This uses the constant-distance relationship time = distance / speed.

Step-by-Step Solution:
T_C = 56 min.T_A = 56 / 6 = 28/3 min = 9 1/3 min.

Verification / Alternative check:
Because A is 6 times faster than C, A should take one-sixth of C's time. 56/6 equals 9 minutes 20 seconds, which is 28/3 minutes.

Why Other Options Are Wrong:
7 min is too small (would imply A is 8 times C); other options do not reflect the 6x speed relationship.

Common Pitfalls:
Multiplying instead of dividing the time by the speed factor or misreading the chained speed multipliers.

Final Answer:
28/3 min