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Select the correct answerA and B are 15 kms apart and when travelling towards each other meet after half an hour where as they meet two and a half hours later if they travel in the same direction. The faster of the two travels at the speed of?Options15 km10 km8 km18 km

Question

Select the correct answerA and B are 15 kms apart and when travelling towards each other meet after half an hour where as they meet two and a half hours later if they travel in the same direction. The faster of the two travels at the speed of?Options15 km10 km8 km18 km

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Solution

Let's solve this step by step:

  1. When A and B are travelling towards each other, they meet after half an hour. This means that the combined speed of A and B is 15 km/0.5 hour = 30 km/hour.

  2. When A and B are travelling in the same direction, they meet two and a half hours later. This means that the difference in speed of A and B is 15 km/2.5 hours = 6 km/hour.

  3. Now, we can set up the following system of equations to solve for the speeds of A and B:

    A + B = 30 (from the first condition)

    A - B = 6 (from the second condition)

  4. Adding these two equations together, we get 2A = 36, so A = 18 km/hour.

  5. Substituting A = 18 into the first equation, we get 18 + B = 30, so B = 12 km/hour.

So, the faster of the two, A, travels at the speed of 18 km/hour. Therefore, the correct answer is 18 km.

This problem has been solved

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