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 950-meter head start. When the start gun is fired the hare begins running at a constant speed of 9.5 meters per second and the tortoise begins crawling at a constant speed of 4 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 number of seconds, n , since the start gun was fired.b. Preview Define a formula to determine the distance (in meters) of the hare from the starting line, h , in terms of the number of seconds, n since the start gun was fired.c. Preview Define a formula that determines the number of meters the tortoise is ahead of the hare, d , with the number of seconds, n , since the start gun was fired.d. Preview Who finishes the race first?

Answer 1

A. t=4n+950

B. h=9.5n

C. d=9.5n-(4n+950)

D. The tortoise will finish first.

Explanation:

To find the first two equations, we put the rate at which they are traveling in front of the n, and then add where they start. Since the tortoise gets a 950 meter head start, we add 950. The hare is starting at the start line so we don't need to add anything.

For answer c, we need to subtract the two equations from each other to figure out when they would pass each other. d=(equation h)-(equation t).

For the final answer, all you need to do is plug the first two equations into a graph, and then find where each line is at the point of y 1,600. (To make the graphs I replaced the n with x and the t and h with y.) Using this, we are able to see who got there first, which was the tortoise.