Question

Arup and Swarup leave point A at 8 AM to point B. To reach B, they have to walk the first 2 km, then travel 4 km by boat and complete the final 20 km by car. Arup and Swarup walk at a constant speed of 4 km/hr and 5 km/hr respectively. Each rows his boat for 30 minutes. Arup drives his car at a constant speed of 50 km/hr while Swarup drives at 40 km/hr. If no time is wasted in transit, when will they meet again?

Accepted Answer

D. Walking time: Arup: $\frac{2}{4} = 30$ mins. Swarup: $\frac{2}{5} = 24$ mins. Boat time: Both take 30 mins. Thus, Swarup finishes boat leg at $24 + 30 = 54$ mins after 8 AM and starts driving at $8:54$ AM. Arup finishes boat leg at $30 + 30 = 60$ mins after 8 AM and starts driving at $9:00$ AM. In those 6 mins (8:54 to 9:00 AM), Swarup drives $40 	imes \frac{6}{60} = 4$ km ahead. Relative speed during car driving = $50 - 40 = 10$ km/hr. Time taken by Arup to catch Swarup = $\frac{4}{10}$ hours = 24 minutes. Since Arup started driving at 9:00 AM, they meet at $9:00 + 24 	ext{ mins} = 9:24$ AM.

Meeting Time after Multi-modal Travel

Explanation

Practise this under exam conditions