Just Jogging Learning Task (Rational Expressions) printable pdf download

GPS Training Days 1, 2 and 3 Mathematics 1

Research and Resource Manual

Just Jogging Learning Task

(Rational Expressions)

For distances of 12 miles or less, a certain jogger can maintain an average speed of 6 miles per

hour while running on level ground.

1. If this jogger runs around a level track at an average speed of 6 mph, how long in hours will

the jogger take to run each of the following distances? [Express your answers as fractions of

an hour in simplest form, the decimal equivalent of that fraction, and the equivalent number

of minutes.] (a) 3 miles (b) 9 miles (c) 1 mile (d)

mile (e)

mile

2. Analyze your work in Question 1. Each answer can be found by using the number of miles, a

single operation, and the number 6. What operation should be used? Write an algebraic

expression for the time it takes in hours for this jogger to run x miles on level ground at an

average speed of 6 miles per hour.

3. Each day this jogger warms up with stretching exercises for 15 minutes, jogs for a while, and

then cools down for 15 minutes. How long would this exercise routine take, in hours, if the

jogger ran for 5 miles? [Express your answer as a fraction in simplest form.]

4. Let T represent the total time in hours it takes for this workout routine when the jogger runs

for x miles. Write a formula for calculating T given x, where, as in Question 2, x is number

of miles the jogger runs. Express the formula for T as a single algebraic fraction.

5. If the jogger skipped the warm-up and cool-down period and used this additional time to jog,

how many more miles would be covered? Does this answer have any connection to the

answer to question 4 above?

Suppose this same jogger decides to go to a local park and use one of the paths there for the

workout routine one day each week. This path is a gently sloping one that winds its way to the

top of a hill.

6. If the jogger can run at an average speed of 5.5 miles per hour up the slope and 6.5 miles per

hour going down the slope, how long, in hours, will it take for the jogger to cover 2 miles by

going uphill for 1 mile and then returning 1 mile back down the hill? Give an exact answer

expressed as a fraction in simplest terms and then give a decimal approximation correct to

three decimal places.

7. If the jogger can run at an average speed of 5.3 miles per hour up the slope and 6.7 miles per

hour going down the slope, how long, in hours, will it take for the jogger to cover 2 miles by

going uphill for 1 mile and then returning 1 mile back down the hill? Give an exact answer

expressed as a fraction in simplest terms and then give a decimal approximation correct to

three decimal places.

Just Jogging Learning Task (Rational Expressions)