Multiple choice

Two places A and B are 100 km apart on a highway. One car starts from A and the other from B at the same time. If the cars travel in the same direction at a constant speed, they meet in 5 hours. If the cars travel towards each other, they meet in 1 hour. What is the speed of the car running faster?

  1. 60 km/hr

  2. 50 km/hr

  3. 40 km/hr

  4. 32 km/hr
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A Correct answer
Explanation

Let speeds be u and v (u > v). Same direction: 100 / (u - v) = 5, so u - v = 20. Opposite direction: 100 / (u + v) = 1, so u + v = 100. Adding equations: 2u = 120, u = 60.

AI explanation

Using the relative speed concept for two bodies moving towards each other, their relative speed is the sum of their speeds, so the sum of their speeds is 100 divided by 1, which is 100 km/hr. When moving in the same direction, their relative speed is the difference of their speeds, which equals 100 divided by 5, giving 20 km/hr. Solving the equations v1 + v2 = 100 and v1 - v2 = 20 gives v1 = 60 and v2 = 40. Therefore, the speed of the faster car is 60 km/hr.

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