A tortoise and hare compete in a 2000-yard race. The fast hare starts at the starting line and gives the tortoise a 700-yard head start. When the starting gun is fired the hare and tortoise begin running at constant speeds. The hare reaches the 100 yard-mark in 4 seconds. The tortoise crawls to the 800 yard-mark in 10 seconds Let T be the tortoise's distance and H the hare's distance from the starting line, in yards, x seconds since the race began. (a) Depict the race on a numberline. Label the starting places, end, and 3 distances. (b) What is the tortoise's speed? How far from the starting line is the tortoise 1 second after the race began? Include units. (c) If Δx=1, what does ΔH equal? (d) Write an equation for H in terms of x. (e) Write an equation for T in terms of x. (f) (no partial credit) For each box, check the box if the quantities are proportional. H,xΔH,ΔxT,xΔT,Δx (g) Who finishes the race first? Justify completely.