A tortoise and a hare are competing in a race around a 1600-meter track. The arr

Question

A tortoise and a hare are competing in a race around a 1600-meter track. The arrogant hare decides to let the tortoise have a 740-meter head start. When the start gun is fired the hare begins running at a constant speed of 9 meters per second and the tortoise begins crawling at a constant speed of 5 meters per second.

a. Define a formula to determine the distance (in meters) of the tortoise from the starting line, t, in terms of the varying number of seconds, n, since the start gun was fired.

b. Define a formula to determine the distance (in meters) of the hare from the starting line, h, in terms of the varying number of seconds, n since the start gun was fired.

c. Define a formula that determines the number of meters the tortoise is ahead of the hare, d, in terms of the varying number of seconds, n, since the start gun was fired.

Explanation / Answer

a) The hare's speed is 9 m/s, so after n seconds the hare has traveled 9n meters.
b) The tortoise's speed is 5 m/s, so after n seconds the tortoise has traveled 5n meters. This, plus the head start, gives the tortoise's position as 5n+740 meters.
c) The amount by which the tortoise is ahead at n seconds is then (5n+740) - 9n meters, or (740-4n) meters.

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