Math Problem Statement

An escalator moves towards the top level at the rate of 11 ft.sec and its length is 140 feet. If a person walks on the moving escalator at the rate of 3 feet per second towards the top level, how much time does he take to cover the entire length.

Solution

To find out how much time the person takes to cover the entire length of the escalator, we need to combine the speeds of the escalator and the person.

Given:

  • Speed of the escalator: 11ft/sec11 \, \text{ft/sec}
  • Speed of the person walking on the escalator: 3ft/sec3 \, \text{ft/sec}
  • Length of the escalator: 140ft140 \, \text{ft}

Since the person is walking in the same direction as the escalator is moving, we add the two speeds:

Total speed=11ft/sec+3ft/sec=14ft/sec\text{Total speed} = 11 \, \text{ft/sec} + 3 \, \text{ft/sec} = 14 \, \text{ft/sec}

Now, to find the time taken to cover the length of the escalator, we use the formula:

Time=DistanceSpeed\text{Time} = \frac{\text{Distance}}{\text{Speed}}

Time=140ft14ft/sec=10seconds\text{Time} = \frac{140 \, \text{ft}}{14 \, \text{ft/sec}} = 10 \, \text{seconds}

Answer:

The person takes 10 seconds to cover the entire length of the escalator.

Would you like further details or clarifications?

Here are 5 related questions to explore:

  1. What if the escalator was moving slower, at 5 ft/sec? How would the time change?
  2. If the person walks in the opposite direction of the escalator, how would you calculate the time taken?
  3. How long would it take if the person stood still on the escalator?
  4. What would happen if the person walks at 6 ft/sec instead of 3 ft/sec?
  5. How far will the person walk in 5 seconds if the escalator is turned off?

Tip: When solving motion problems involving multiple moving elements, always consider their relative speeds.

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Math Problem Analysis

Mathematical Concepts

Speed and Distance
Linear Motion
Rate of Change

Formulas

Time = Distance / Speed

Theorems

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Suitable Grade Level

Grades 6-8