Time, Speed and Distance Question 5 - CAT 2023
Arvind travels from town A to town B, and Surbhi from town B to town A, both starting at the same time along the same route. After meeting each other, Arvind takes 6 hours to reach town B while Surbhi takes 24 hours to reach town A. If Arvind travelled at a speed of 54 km/h, then the distance, in km, between town A and town B is:
Step-by-Step Explanation
Apply the Meeting and Destination Theorem:
When two travelers start simultaneously from opposite points and move toward each other, the time t elapsed from their start to the meeting point is the geometric mean of the individual times they take to reach their destinations after crossing paths (t₁ and t₂):
t = √(t₁ × t₂)
We are given t₁ = 6 hours (Arvind) and t₂ = 24 hours (Surbhi).
t = √(6 × 24) = √144 = 12 hours
Determine Surbhi's Speed:
The speed ratio of two travelers is inversely proportional to the square root of their travel times after meeting:
Speed₍Arvind₎ / Speed₍Surbhi₎ = √(t₂/t₁)
= √(24/6) = √4 = 2
Given Arvind's speed is 54 km/h:
Speed₍Surbhi₎ = 54/2 = 27 km/h
Calculate the Total Distance:
They travel toward each other for 12 hours before meeting, meaning their combined relative speed covers the entire distance during this time:
Total Distance = (Speed₍Arvind₎ + Speed₍Surbhi₎) × t
= (54 + 27) × 12 = 81 × 12 = 972 km
Correct Answer: 972
💡 FundaMakers Tip:
The formulas t = √(t₁ × t₂) and s₁/s₂ = √(t₂/t₁) are powerful tools for managing post-meeting scenarios. Memorize them to handle simultaneous reciprocal journeys efficiently, bypassing multi-step linear distance tracking entirely.