Person K is 50% faster than person L. L starts a journey at 9:00 a.m. from one point, and K starts at 10:00 a.m. from another point such that L and K are initially 300 km apart. L travels at 50 km/h, and both travel towards each other in opposite directions. At what clock time will they meet?

Introduction / Context:
This question deals with two travelers starting at different times from locations that are a fixed distance apart and moving towards each other. It examines the ability to handle different starting times, compute speeds from percentage relationships, and determine the meeting time using relative speed. Such problems are common in quantitative aptitude tests focusing on time, speed, and distance.

Given Data / Assumptions:

• L starts at 9:00 a.m.
• K starts at 10:00 a.m.
• Initial distance between them = 300 km.
• L travels at 50 km/h.
• K is 50% faster than L, so K's speed = 1.5 * 50 km/h = 75 km/h.
• They travel towards each other in opposite directions along a straight route.

Concept / Approach:
First, we compute how far L travels alone in the one hour between 9:00 a.m. and 10:00 a.m. This reduces the distance between them. After 10:00 a.m., both K and L move towards each other, and we consider their combined (relative) speed. The time taken for them to meet from 10:00 a.m. onward is equal to remaining distance divided by the sum of their speeds. Finally, we add this time to 10:00 a.m. to get the actual meeting time.

Step-by-Step Solution:
Speed of L = 50 km/h. Speed of K = 1.5 * 50 = 75 km/h. Distance between them at 9:00 a.m. = 300 km. From 9:00 a.m. to 10:00 a.m., only L travels. Distance L covers in 1 hour = 50 * 1 = 50 km. Remaining distance at 10:00 a.m. = 300 - 50 = 250 km. From 10:00 a.m., both travel towards each other. Relative speed = 50 + 75 = 125 km/h. Time to meet from 10:00 a.m. = remaining distance / relative speed = 250 / 125 = 2 hours. Meeting time = 10:00 a.m. + 2 hours = 12:00 p.m. (noon).

Verification / Alternative check:
We can validate by computing their positions at the meeting time. L travels from 9:00 a.m. to 12:00 p.m., which is 3 hours, covering 3 * 50 = 150 km. K travels from 10:00 a.m. to 12:00 p.m., which is 2 hours, covering 2 * 75 = 150 km. Combined, they cover 150 + 150 = 300 km, which equals the initial separation. This confirms that they meet exactly at 12:00 p.m.

Why Other Options Are Wrong:
Meeting times of 11:00 a.m., 11:30 a.m., 1:00 p.m., or 2:00 p.m. do not match the distances covered given the stated speeds and initial separation. If they met earlier than 12:00 p.m., the joint distance would be less than 300 km; if they met later, the joint distance would exceed 300 km. Only 12:00 p.m. matches all conditions.

Common Pitfalls:
Some students forget to account for the one hour head start of L and apply relative speed from 9:00 a.m., which gives an incorrect meeting time. Others misinterpret 50% faster and add 50 km/h instead of multiplying by 1.5. Carefully computing the head start distance and then using the sum of speeds from the second start time is the correct approach.

Final Answer:
K and L will meet at 12 p.m. (noon).