a. Running uphill the jogger runs c mph slower than 6 mph. Write an expression representing a speed of c mph slower than 6 mph. ___________
[tex]6 - c[/tex]
b. Write an algebraic expression that represents the time it takes to run 1 mile uphill at a speed that is c mph slower than 6 mph. ___________ (Refer to #1a for help.)
[tex]\dfrac{1}{6 - c}[/tex]
c. Running downhill the jogger runs c mph faster than 6 mph. Write an expression represents a speed of c mph faster than 6 mph. ___________
[tex]6 + c[/tex]
d. Write an algebraic expression that represents the time it takes to run 1 mile downhill at a speed that is c mph faster than 6 mph. ___________ (Refer to #1b for help.)
[tex]\dfrac{1}{6 + c}[/tex]
e. Use your answers to b and d to write an algebraic expression for the total time, in hours, that it takes the jogger to cover 2 miles by going uphill for 1 mile and then returning 1 mile back down the hill.
[tex]\dfrac{1}{6 - c} + \dfrac{1}{6 + c}[/tex]
f. Simplify your answer to part e into a single algebraic fraction. (Remember to find a common denominator first.)
[tex]\dfrac{1}{6 - c} +\dfrac{1}{6 + c} = \dfrac{(6+c)+(6-c)}{(6 - c)(6+c)} = \dfrac{12}{36 - c^2}[/tex]
Parts g and h refer to "#1" and "#2," presumably particular examples, but not given in the question so you're on your own with those.
g. What is the value of c for #1? (How much slower does she run uphill?) ________ Use this c to test your answer to part f. (Check that it gives the correct answer for #1c.)
h. What is the value of c for #2? (How much slower does she run uphill? ) ________ Use this c to test your answer to part f. (Check that it gives the correct answer for #2.)
