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)
We can start by defining some variables:
- Let x be the number of minutes Jacob runs on the treadmill
- Let y be the number of minutes Jacob does freehand exercises
Based on the problem statement, we know that:
- Jacob spends a total of 60 minutes in the gym, so x + y = 60
- Jacob runs on the treadmill for 30 minutes longer than he does freehand exercises, so x = y + 30
These two equations form a system of linear equations:
x + y = 60
x = y + 30
We can solve for y in the second equation and substitute into the first equation:
x = y + 30
y = x - 30
x + (x - 30) = 60
2x - 30 = 60
2x = 90
x = 45
So Jacob runs on the treadmill for 45 minutes and does freehand exercises for y = x - 30 = 15 minutes.
Therefore, the pair of linear equations that show the relationship between the number of minutes Jacob does freehand exercises (y) and the number of minutes he runs on the treadmill (x) are:
x + y = 60
x = y + 30
Let's define the variables as follows:
x = number of minutes Jacob runs on the treadmill
y = number of minutes Jacob does freehand exercises
We know that Jacob spends a total of 60 minutes in the gym every day, so we have the equation:
x + y = 60
We also know that Jacob runs on the treadmill for 30 minutes longer than he does freehand exercises, so we have the equation:
x = y + 30
These two equations show the relationship between the number of minutes Jacob does freehand exercises (y) and the number of minutes he runs on the treadmill (x).