Multiple choice

Two friends, Akash and Balram, decide to embark on a unique road trip adventure. Akash starts driving north from their starting point at a steady speed of 15 km/hr, while Balram sets off in east direction at a speed that is three times faster than Akash's from the same point. After 30 minutes, Akash sends a message to Balram, saying he just passed by a lakeside park. Then, 15 minutes later, Balram excitedly messages Akash that he is currently at a charming countryside diner. As time goes on, both Akash and Balram eventually decide to stop their cars at the same moment. If the direct distance between their current positions is 120 km, how far (in km) is Balram now from that lakeside park?

  1. 84.54

  2. 94.54

  3. 101.34

  4. 114.40

  5. a
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Akash speed = 15 km/h. Balram speed = 45 km/h. Distance = sqrt((15*t)^2 + (45*t)^2) = 120. t*sqrt(225 + 2025) = 120. t*sqrt(2250) = 120. t = 120 / 47.43 = 2.53 hours. Balram's position = (45*2.53, 0) = (113.85, 0). Lakeside park is at (0, 15*0.5) = (0, 7.5). Distance = sqrt(113.85^2 + 7.5^2) = 114.1. The answer 114.40 is the closest.

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