A fox sees a rabbit 35 feet away and starts chasing it. As soon as the fox starts moving, the rabbit sees it and starts running away at a speed of 40 feet per second.
What should the fox’s speed be to catch up to the rabbit?
The correct answer and explanation is:
To catch the rabbit, the fox must cover the 35 feet separating them and maintain a speed that allows it to close the gap as the rabbit runs away.
Let’s break it down:
- The rabbit is running at 40 feet per second.
- The fox starts at a distance of 35 feet away from the rabbit.
The fox’s speed should be greater than the rabbit’s speed to catch up. If the fox runs at the same speed, it will never close the gap since they are both moving at the same rate.
To calculate how fast the fox needs to run, we need to consider the fact that the fox needs to cover the initial 35 feet and then match the rabbit’s speed in order to catch it.
Now, imagine that the fox is running at a speed of 40 feet per second (the same as the rabbit). In that case, the distance between the two would remain constant, so the fox would never catch up.
But if the fox runs faster than 40 feet per second, it will begin to close the gap. For example, if the fox runs at a speed of 50 feet per second, it will gain on the rabbit by 10 feet every second. At this rate, the fox will close the 35-foot gap in 3.5 seconds (35 ÷ 10 = 3.5 seconds).
Thus, the fox’s speed should be greater than 40 feet per second to catch the rabbit. In general, to guarantee the fox catches the rabbit, its speed must be at least 40 feet per second plus some additional amount depending on how quickly it wants to close the gap.