Question

Now let’s generalize. 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. ___________

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.)
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. ___________
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.)
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.
f. Simplify your answer to part e into a single algebraic fraction. (Remember to find a common denominator first.)
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.)

Answer 1

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. ___________


`6 - c`

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.)


`(1)/(6 - c)`

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. ___________


`6 + c`

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.)


`(1)/(6 + c)`


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.


`(1)/(6 - c) + (1)/(6 + c)`

f. Simplify your answer to part e into a single algebraic fraction. (Remember to find a common denominator first.)


`(1)/(6 - c) +(1)/(6 + c) = ((6+c)+(6-c))/((6 - c)(6+c)) = (12)/(36 - c^2)`

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.)