Shard covers two-thirds of a journey at 4 km/h and the remaining one-third at 5 km/h. If his total time is 42 minutes, what is the total distance?

Introduction / Context:
When segments of a trip are specified as fractions of the total distance with different speeds, compute total time as a sum of fractional-distance time contributions to solve for the total distance.

Given Data / Assumptions:

• (2/3) of distance at 4 km/h.
• (1/3) of distance at 5 km/h.
• Total time = 42 minutes = 0.7 hour.

Concept / Approach:
Let total distance be D. Then time = (2D/3)/4 + (D/3)/5. Set equal to 0.7 hour and solve for D.

Step-by-Step Solution:

Verification / Alternative check:
Time check: (2 km at 4) = 0.5 h; (1 km at 5) = 0.2 h; total = 0.7 h (42 minutes).

Why Other Options Are Wrong:
They correspond to misadding the fractional time terms or misreading minutes vs hours.

Common Pitfalls:
Forgetting to convert 42 minutes to hours; mixing up fractional distance weights.

Final Answer:
3 km