Multiple choice

Sohan is driving at a speed of 60 km/h along a highway. Mohan is 96 meters behind Sohan and also driving in the same direction as Sohan. At the same time, Rohan is driving towards them from the opposite direction at a speed of 40 km/h and is 500 meters away from Sohan. At what speed, in km/h, should Mohan drive so that all three vehicles cross each other at the same time?

  1. 59.7 km/hr

  2. 95.7 km/hr

  3. 79.2 km/hr

  4. 97.5 km/hr

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

Let t be the time to cross. Sohan is at 60t. Mohan is at -0.096 + vt. Rohan is at 0.5 - 40t. For all to cross at the same point: 60t = -0.096 + vt = 0.5 - 40t. From 60t = 0.5 - 40t, 100t = 0.5, t = 0.005 hours. Substitute t into 60t = -0.096 + v(0.005): 0.3 = -0.096 + 0.005v, 0.396 = 0.005v, v = 79.2 km/h.

AI explanation

Sohan and Rohan are moving towards each other with a relative speed of 100 km/h, which is 250/9 meters per second, to cover the 500 meter gap between them. They will meet in 500 divided by 250/9, which equals 18 seconds. For Mohan to cover the 96 meter gap to Sohan in the same 18 seconds, his relative speed to Sohan must be 96 divided by 18, which is 16/3 meters per second, or 19.2 km/h. Adding this relative speed to Sohan's speed of 60 km/h gives Mohan's required speed of 79.2 km/h.

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