Time, Speed and Distance Question 2 - CAT 2023
Ravi is driving at a speed of 40 km/h on a road. Vijay is 54 meters behind Ravi and driving in the same direction as Ravi. Ashok is driving along the same road from the opposite direction at a speed of 50 km/h and is 225 meters away from Ravi. The speed, in km/h, at which Vijay should drive so that all three cross each other at the same time, is:
Step-by-Step Explanation
Analyze the crossing event for Ravi and Ashok:
Ravi and Ashok are driving toward each other, so their relative speed is the sum of their individual speeds.
Relative Speed = 40 km/h + 50 km/h = 90 km/h
Convert this to meters per second:
90 × 5/18 = 25 m/s
They are separated by 225 meters, so the time it takes for them to meet is:
Time to meet = 225 meters / 25 m/s = 9 seconds
Track Ravi's position during these 9 seconds:
Ravi's Speed in m/s = 40 × 5/18 = 100/9 m/s
Distance covered by Ravi = 100/9 × 9 = 100 meters
Determine Vijay's required speed:
For all three to meet at the exact same moment, Vijay must catch up to the meeting point in those same 9 seconds. Since Vijay started 54 meters behind Ravi, his total travel distance is:
Vijay's Distance = 54 + 100 = 154 meters
Vijay's Speed = 154/9 m/s
Convert back to km/h:
Vijay's Speed = 154/9 × 18/5
= 154 × 2/5 = 308/5 = 61.6 km/h
Correct Option: C
💡 FundaMakers Tip:
When multiple moving objects cross at a single point, time is the common link. Find the meeting time of the two objects whose initial positions and speeds are completely known (Ravi and Ashok). Once you find that the event takes exactly 9 seconds, the problem simplifies to calculating the basic speed needed to cover a fixed distance over that time.