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9. A cheetah is located 100 yards away from an antelope. The cheetah begins running on a straight path toward the antelope at a constant speed of 30 yards per second. At the same time, the antelope begins running away from the cheetah at a constant speed of 25 yards per second. If both animals continue to run on a straight path at the same speeds, how long will it take for the cheetah to catch up to the antelope?​

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It takes 20 seconds for the cheetah to catch up to the antelope

Speed is the ratio of distance to time taken. It is given by:

Speed = distance / time

Let d represent the distance covered by the cheetah at time t, hence:

30 = d / t

t = d / 30

The antelope is 100 yards away, hence:

25 = (d - 100) / t

t = (d - 100)/25

d/30 = (d - 100)/25

25d = 30d - 3000

d = 600 yards

t = d/30 = 600/30 = 20 seconds

It takes 20 seconds for the cheetah to catch up to the antelope

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