Time, Speed and Distance Question 3 - CAT 2021
Mira and Amal walk along a circular track, starting from the same point at the same time. If they walk in the same direction, then in 45 minutes, Amal completes exactly 3 more rounds than Mira. If they walk in opposite directions, then they meet for the first time exactly after 3 minutes. The number of rounds Mira walks in one hour is:
Step-by-Step Explanation
Let us solve this problem by working entirely with the unit rounds per minute.
Analyze the Same-Direction Scenario:
Amal completes exactly 3 more rounds than Mira in 45 minutes. This means Amal laps Mira 3 times, establishing their relative tracking speed:
Relative Speed (Same Direction) = vᴬ − vᴹ = 3/45 = 1/15 rounds/min
Analyze the Opposite-Direction Scenario:
When moving in opposite directions, they meet for the first time in 3 minutes, meaning their combined speeds cover exactly 1 complete round:
Relative Speed (Opposite Direction) = vᴬ + vᴹ = 1/3 rounds/min
Isolate Mira's Speed (vᴹ):
Subtract the same-direction equation from the opposite-direction equation:
(vᴬ + vᴹ) − (vᴬ − vᴹ) = 1/3 − 1/15
2vᴹ = 5/15 − 1/15 = 4/15
vᴹ = 2/15 rounds per minute
Calculate Mira's Total Rounds in One Hour (60 minutes):
Total Rounds = 2/15 × 60 = 2 × 4 = 8 rounds
Correct Answer: 8
💡 FundaMakers Tip:
Do not introduce a circumference variable like C or track physical distances in meters for circular track problems when the question asks for a final answer in rounds. Defining speeds as rounds per minute simplifies the algebra down to a basic two-variable linear system that can be solved mentally.