Answer:
40 minutes
Explanation:
To determine the length of time that at least part of the shadow of the tree falls on Wok's building, we need to consider the height of the tree, the distance between the tree and the building, and the angle of elevation of the sun.
Let's start by visualizing the situation with a diagram:
```
Sun
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|--------------------------| <- Shade tree (20 m tall)
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|--------------------------| <- Wok's apartment building (10 m tall)
```
Based on the information given, we know that the shadow of the tree falls directly toward the building. This means that the shadow will touch the building when the angle of elevation of the sun is such that the top of the tree is in line with the top of the building.
Let's represent this situation in another diagram:
```
Sun
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|--------------------------| <- Shade tree (20 m tall)
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|--------------------------| <- Wok's apartment building (10 m tall)
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| | <- Shadow of the tree touching the building
```
To calculate the length of time the shadow falls on Wok's building, we need to find the time it takes for the top of the tree to align with the top of the building.
Given that the angle of elevation of the sun increases by 15° per hour, we can calculate the time it takes for the angle of elevation of the sun to increase by 10° (the height difference between the tree and the building).
10° / 15° per hour = 2/3 hour = 40 minutes
Therefore, at least part of the shadow of the tree falls on Wok's building for 40 minutes