The Correct Answer and Explanation is:
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Answer: The fox’s speed should be at least 43.5 feet per second.
Explanation:
To solve this problem, we need to determine the minimum speed the fox must maintain to close the distance to the rabbit within the given timeframe.
First, let’s establish the conditions for the fox to catch the rabbit. When the fox catches the rabbit, they will both be at the same location. This means the distance traveled by the fox must be equal to the initial 35-foot gap plus the distance the rabbit travels.
The problem states that the catch must happen in “no more than 10 seconds”. To find the minimum speed the fox requires, we should consider the longest possible time allowed for the chase, which is exactly 10 seconds.
Let’s calculate the total distance the fox needs to cover in those 10 seconds.
- First, find the distance the rabbit runs in 10 seconds. Using the formula Distance = Speed × Time:
Distance traveled by rabbit = 40 feet/second × 10 seconds = 400 feet. - Next, calculate the rabbit’s final position relative to the fox’s starting point. The rabbit had a 35-foot head start and then ran an additional 400 feet.
Total distance from fox’s start = 35 feet + 400 feet = 435 feet.
For the fox to catch the rabbit at this exact moment, it must travel this total distance of 435 feet in 10 seconds.
Now, we can calculate the required speed for the fox:
Fox’s Speed = Total Distance / Time
Fox’s Speed = 435 feet / 10 seconds
Fox’s Speed = 43.5 feet per second.
This value of 43.5 feet per second is the minimum speed the fox must have. If the fox runs at this speed, it will catch the rabbit in exactly 10 seconds. If it runs any faster, it will catch the rabbit in less than 10 seconds, which also satisfies the condition. Therefore, the fox’s speed must be 43.5 feet per second or greater.
