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Let's break down the problem:

1. When Moody walks at his normal speed on the escalator, it takes him 30 seconds to complete the ride.
2. When he walks at twice his normal speed, it takes him only 20 seconds.
3. We want to find the time needed if Moody stands still on the escalator.

### Analysis
Let:
- \( S \) be the speed of the escalator.
- \( W \) be Moody's normal walking speed.
- \( L \) be the length of the escalator.

From the problem, when Moody walks at his normal speed:
\[ \text{Time} = \frac{L}{W + S} = 30 \]

When he walks at twice his normal speed:
\[ \text{Time} = \frac{L}{2W + S} = 20 \]

We can solve these two equations to find \( L \), \( W \), and \( S \).

### Solving the Equations
1. From the first equation: 
\[ L = 30(W + S) \]

2. From the second equation:
\[ L = 20(2W + S) \]

Setting them equal:
\[ 30(W + S) = 20(2W + S) \]

Simplifying:
\[ 30W + 30S = 40W + 20S \]
\[ 10S = 10W \]
\[ S = W \]

### Finding the Time when Moody Stands Still
If Moody stands still, his speed is zero, so the time to finish riding the escalator is simply:

\[ \text{Time} = \frac{L}{S} \]

Substitute \( L = 30(W + S) \) and \( S = W \):

\[ \text{Time} = \frac{30(W + W)}{W} \]
\[ \text{Time} = 60 \, \text{seconds} \]

Thus, the time needed if Moody stands still is:

### **60 seconds**

Would you like a more detailed explanation or have any follow-up questions?

### Relative Questions
1. How can you generalize this formula for different speeds?
2. What if Moody walked at three times his normal speed?
3. How would the time change if the escalator was twice as long?
4. What happens if the escalator's speed increases?
5. Can this approach be used for variable-speed escalators?

### Tip
When dealing with relative motion, always set up equations for each scenario to solve for unknown variables efficiently.

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:

Learn how to calculate the time taken to ride an escalator when standing still, based on different walking speeds and relative motion concepts. The problem involves solving linear equations using algebraic methods. Suitable for Grades 8-10.

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