Question

Jacob spends 60 minutes in the gym every day doing freehand exercises and running on the treadmill. He runs on the treadmill for 30 minutes longer than he does freehand exercises.


Part A: Write a pair of linear equations to show the relationship between the number of minutes Jacob does freehand exercises (y) and the number of minutes he runs on the treadmill (x).


Part B: How much time does Jacob spend doing freehand exercises? Show your work.


Part C: Is it possible for Jacob to have spent 40 minutes running on the treadmill if he spends exactly 60 minutes total at the gym and runs on the treadmill for 30 minutes longer than he does freehand exercises? Explain your reasoning.

Answer 1

Jacob runs on the treadmill for 45 minutes and he does free hand exercises for 15 minutes.

Equation

Equation is an expression used to show the relationship between two or more numbers and variables.

Let x represent the number of minutes Jacob runs on treadmill and y represent the number of minutes on free hand exercise.

Since he spends 60 minute, hence:

x + y = 60    (1)

Also:

x = y + 30   (2)

From equation 1 and 2:

x = 45, y = 15

Jacob runs on the treadmill for 45 minutes and he does free hand exercises for 15 minutes.

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