A cheetah is 300 feet from its prey. It starts to sprint toward its prey at 90 feet per second. At the same time, the prey starts to sprint at 70 feet per second. When will the cheetah catch its prey?

Xp = 300 + 70 t (Prey location)

Xc = 90 t (Cheetah location)
t is in seonds and the X's are in feet.

The prey will be caught when Xp = Xc

300 + 70 t = 90 t
20 t = 300

Solve for t

To determine when the cheetah catches its prey, we need to find the time it takes for both the cheetah and the prey to cover the distance between them.

Let's calculate the time it takes for the cheetah to catch the prey:

Distance between the cheetah and the prey = 300 feet
Cheetah's speed = 90 feet per second

Using the formula: time = distance / speed

Time it takes for the cheetah to catch its prey = 300 feet / 90 feet per second
Time = 3.33 seconds (rounded to two decimal places)

Now let's calculate the time it takes for the prey to run:

Prey's speed = 70 feet per second

Using the same formula:

Time it takes for the prey to run = 300 feet / 70 feet per second
Time = 4.29 seconds (rounded to two decimal places)

Since the cheetah catches up to the prey first (in 3.33 seconds) before the prey can escape (in 4.29 seconds), we can conclude that the cheetah catches its prey in approximately 3.33 seconds.