Question

A man walking upward on a staircase at the speed of x steps per second takes a total time of y seconds to reach the top. At what speed (in steps per second) he should walk to reach at the top in \(\frac{y}{3}\) seconds?

• A. \(\frac{3}{x}\)
• B. \(\frac{3x}{2}\)
• C. \(2x\)
• D. \(3x\)

Answer 1

The Correct Option is D

Step 1: Calculate the Number of Steps

The number of steps taken to reach the top is: 

\[ \text{Number of steps} = x \times y \]

Step 2: Determine the New Speed

To cover the same number of steps in \(\frac{y}{3}\) seconds, the new speed must be:

\[ \text{New speed} = \frac{\text{Total steps}}{\text{Time taken}} \]

\[ = \frac{x \times y}{\frac{y}{3}} \]

Conclusion:

The required speed is \(3x\) steps per second.