Aryan runs at a speed on 40 metre/ minute. Rahul follows him after an interval of 5 minutes and runs at a speed of 50 metre/minute. Rahul’s dog runs at a speed of 60 metre/minute and starts along with Rahul. The dog reaches Aryan and then comes back to Rahul, and continues to do so till Rahul reaches Aryan. What is the total distance covered by the dog?

When Rahul starts 5 minutes later, Aryan has a head start of 40 m/min × 5 min = 200 m (given in the worked solution) . Rahul’s speed relative to Aryan is 50 − 40 = 10 m/min, so time for Rahul to catch Aryan = head start / relative speed = 200/10 = 20 minutes . The dog runs for the entire period Rahul takes to reach Aryan. Using the relation distance = speed × time, the dog’s distance = 60 m/min × 20 min = 1200 m [1]. Hence the total distance covered by the dog is 1200 metres (option 4).

Sources

1. [1] Science-Class VII . NCERT(Revised ed 2025) > Chapter 8: Measurement of Time and Motion > 8.3 Speed > p. 113