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Walking at 34 of his usual speed, a man is 1.5 hours late. His usual time to cover the same distance, (in hours) is?

Question

Walking at 34 of his usual speed, a man is 1.5 hours late. His usual time to cover the same distance, (in hours) is?

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Solution

To solve this problem, we need to understand that speed is inversely proportional to time taken when the distance is constant.

Let's denote:

  • The man's usual speed as 's' (in km/hour or any other unit)
  • The man's usual time to cover the distance as 't' (in hours)

When the man walks at 3/4 of his usual speed, his speed becomes 3s/4.

Since speed is inversely proportional to time, the time taken when he walks at this slower speed is inversely proportional to 3s/4, which means the time taken is 4t/3.

According to the problem, this slower speed makes the man 1.5 hours late. This means that 4t/3 = t + 1.5.

We can solve this equation for 't' to find the man's usual time to cover the distance:

4t = 3t + 4.5 4t - 3t = 4.5 t = 4.5 hours

So, the man's usual time to cover the same distance is 4.5 hours.

This problem has been solved

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