A spider climbs 62 1/2% of the height of the pole in one hour and the next hour it covers 12 1/2% of the remaining height. If the total height is 192 m, then what is the distance c... A spider climbs 62 1/2% of the height of the pole in one hour and the next hour it covers 12 1/2% of the remaining height. If the total height is 192 m, then what is the distance climbed in the second hour?
Understand the Problem
The question is asking for the distance that a spider climbs during the second hour after it has already climbed a portion of the total height of the pole in the first hour. We will first calculate the height of the pole that the spider climbs in the first hour, then determine the remaining height after the first hour, and finally calculate the distance climbed in the second hour based on the remaining height.
Answer
The distance climbed in the second hour is $d_2 = r$ meters.
Answer for screen readers
The distance the spider climbs during the second hour is $d_2 = r$ meters, where $r$ is the rate of climbing in meters per hour.
Steps to Solve
- Calculate the distance climbed in the first hour
Assume the spider climbs at a rate of $r$ meters per hour. During the first hour, the distance climbed is simply $d_1 = r \cdot 1$.
- Find the total height of the pole
Let’s assume the height of the pole is $H$ meters. After the first hour, the height remaining for the spider to climb is $H - d_1$.
- Calculate the distance climbed in the second hour
During the second hour, the spider will climb the same rate, so the distance climbed in the second hour is $d_2 = r \cdot 1$.
- Determine the height left after the second hour
After the second hour, the total height climbed will be $d_1 + d_2$. The height remaining will be $H - (d_1 + d_2)$, which allows us to see if the spider has reached the top.
The distance the spider climbs during the second hour is $d_2 = r$ meters, where $r$ is the rate of climbing in meters per hour.
More Information
If the spider climbs at a consistent rate and if the height $H$ is sufficient, the spider will consistently climb the same distance each hour. The calculations demonstrate the importance of understanding consistent rates.
Tips
- Confusing the total distance climbed with the portion climbed in each hour. It’s essential to distinguish between total height and height climbed per hour.
- Assuming the rate changes; unless specified, we assume the rate remains constant.
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