Two walkers start together for the same destination. One walks at 3.75 km/h and the other at 3 km/h. If the faster walker arrives 30 minutes earlier, what is the distance to the destination?

Introduction / Context:When two travelers cover the same distance at different constant speeds, the difference in their arrival times equals the distance times the difference of reciprocals of their speeds.

Given Data / Assumptions:

• Speeds: v1 = 3.75 km/h, v2 = 3 km/h.
• Time difference = 0.5 hour.
• Both start simultaneously and go directly to the same point.

Concept / Approach:Let distance be D. Then arrival time difference: D/3 - D/3.75 = 0.5. Solve for D.

Step-by-Step Solution:

Verification / Alternative check:Times: 7.5/3 = 2.5 h; 7.5/3.75 = 2 h; difference = 0.5 h as stated.

Why Other Options Are Wrong:They do not satisfy the exact time-difference equation for the given pair of speeds.

Common Pitfalls:Using average of speeds or average of times; the correct relation uses reciprocals of speeds for fixed distance.

Final Answer:7.5 km