Question:medium

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction.He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction.If Moody decides to stand still on the escalator,then the time,in seconds,needed to finish riding the escalator is

Updated On: Jan 15, 2026
Show Solution

Correct Answer: 60

Solution and Explanation

The problem describes Moody walking on an escalator. The duration of his ride is influenced by his walking pace and the escalator's velocity. The following variables are established:

  • \( W \) = Moody’s standard walking velocity (units per second)
  • \( E \) = Escalator's velocity (units per second)

Step 1: Formulate Equations

The problem provides two scenarios:

- When Moody walks at his standard pace, his combined velocity is \( W + E \). He traverses the escalator in 30 seconds. Therefore, the equation is: \[ (W + E) \times 30 = 1 \]

- When Moody walks at double his standard pace, his combined velocity is \( 2W + E \). He completes the ride in 20 seconds. The equation is: \[ (2W + E) \times 20 = 1 \]

Step 2: Solve the System of Equations

From the first equation: \[ 30(W + E) = 1 \] This simplifies to: \[ 30W + 30E = 1 \] Solving for \( E \): \[ E = \frac{1 - 30W}{30} \] Substitute this expression for \( E \) into the second equation: \[ (2W + \frac{1 - 30W}{30}) \times 20 = 1 \] Simplify the expression inside the parentheses: \[ 2W + \frac{1 - 30W}{30} = \frac{1}{20} \] To eliminate the fraction, multiply the entire equation by 30: \[ 60W + 1 - 30W = \frac{30}{20} \] Combine like terms: \[ 30W + 1 = 1.5 \] Isolate \( 30W \): \[ 30W = 0.5 \] Solve for \( W \): \[ W = \frac{0.5}{30} = \frac{1}{60} \]

Step 3: Determine the Escalator's Velocity (\( E \))

Substitute the calculated value of \( W \) into the expression for \( E \): \[ E = \frac{1 - 30 \times \left( \frac{1}{60} \right)}{30} \] Perform the calculation: \[ E = \frac{1 - 0.5}{30} = \frac{0.5}{30} = \frac{1}{60} \]

Step 4: Calculate the Time Without Walking

If Moody remains stationary, his effective velocity is solely the escalator's velocity, \( E \). The time required to cover the escalator's length is calculated as:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{1}{E} = \frac{1}{\frac{1}{60}} = 60 \text{ seconds} \]

Final Answer:

If Moody stands still on the escalator, the ride duration will be 60 seconds.

Conclusion:

The correct answer is \( \boxed{60} \) seconds.

Was this answer helpful?
0

Top Questions on Time, Speed and Distance

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution