A person weighing 130 pounds will burn 590 calories for every 6 miles that they run (at a particular speed). Assume that Allyson weighs 130 pounds and is running at the specified speed.

a) What does this mean for any change in the number of miles that Allyson runs?

b) How many calories will Allyson burn if she runs 3 miles? 12 miles? 10 miles?

c) If Allyson has burned 73.75 calories, how many miles has she burned? Explain your reasoning.

d) Use delta notation to write a formula that relates the change in the number of calories Allyson has run to the change in the distance (measured in miles) that Allyson has run. Be sure to define your variables.

Jane is walking from her home to work. She walks at a constant speed and travels 30 feet every 8 seconds.

a) Identify two varying quantities.

b) Identify one constant quantity.

c) How long does it take Jane to travel 15 feet? 10 feet? 4 feet? Explain your reasoning.

d) How far does Jane travel in 2 seconds? 5 seconds? Explain your reasoning.

e) How far will Jane travel during any 1-second interval?

f) How long will it take Jane to travel 1 foot?

g) Use delta notation to write a formula that expresses the change in Jane's distance traveled in feet in terms of the change in the number of seconds that Jane had been walking. Be sure to define your variables.