Just Jogging Learning Task (Rational Expressions) (Page 2 of 2) in pdf

Just Jogging Learning Task (Rational Expressions) Page 2

GPS Training Days 1, 2 and 3 Mathematics 1

Research and Resource Manual

8. 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 if the jogger

runs uphill at an average speed that is c miles per hour slower than the level-ground speed of

6 miles per hour and runs downhill at an average speed that is c miles per hour faster than the

level-ground speed of 6 miles per hour. Simplify your answer to a single algebraic fraction.

Verify that your expression gives the correct answers for Questions 6 and 7.

9. The average speed in miles per hour is defined to be the distance in miles divided by the time

in hours spent covering the distance.

(a) What is the jogger’s average speed for a two mile trip on level ground?

(b) What is the jogger’s average speed for the two mile trip in question 6?

(d) Write an expression for the jogger’s average speed over the two-mile trip (one mile up

and one mile down) when the average speed uphill is c miles per hour slower than the

level-ground speed of 6 miles per hour and the average speed downhill at an average

speed that is c miles per hour faster than the level-ground speed of 6 miles per hour.

Express your answer as a simplified algebraic fraction.

(e) Use the expression in part (d) to recalculate your answers for parts (b) and (c)? What

value of c should you use in each part?

10. For what value of c would the jogger’s average speed for the two-mile trip (one mile up and

one mile down) be 4.5 miles per hour? For this value of c, what would be the jogger’s

average rate uphill and downhill?

Just Jogging Learning Task (Rational Expressions) Page 2