Question

A cheetah can run at top speed for only about 20 seconds. If an antelope is too far away for a cheetah to catch it in 20 seconds, the antelope is probably safe. Your friend claims an antelope that is running 60 feet per second that is 120 feet away will not be safe if the cheetah starts running 650 feet behind it. Is your friend correct?

Answer 1

Let's break down

C

Antelope

Initial distance: The antelope is initially 120

Cheetah's starting position: The cheetah starts running 650 feet behind the antelope.

Given this information, let's calculate whether the antelope will be caught by the cheetah:

In the first 20 seconds, the cheetah will cover a distance of (20 seconds) × (Cheetah's top speed). Since the cheetah's top speed is not specified, we'll denote it as "C" for now.

Distance covered by the cheetah = 20C

In the same 20 seconds, the antelope will cover a distance of (20 seconds) × (Antelope's speed).

Distance covered by the antelope = 20 × 60 = 1200 feet

Now, when the cheetah starts running from 650 feet behind the antelope, it will close the initial distance between them at a rate of (Cheetah's speed) - (Antelope's speed) per second.

Rate at which the cheetah closes the gap = C - 60 feet per second

We want to find out if the cheetah can close the 650 feet gap between them within 20 seconds:

Distance covered by the cheetah to close the gap = 20 × (C - 60)

Now, if the cheetah can cover this distance and still have enough time to catch up to the antelope (which would be the remaining distance), then the antelope is not safe. This can be expressed as:

20C + 20 × (C - 60) ≥ 1200 + 650

Solving this equation will tell us if the antelope is safe or not.

However, without knowing the specific top speed of the cheetah (the value of "C"), we cannot provide a definitive answer. If you can provide the cheetah's top speed, I can help you calculate whether the antelope will be caught or not based on the given information.

Explanation: