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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 :

Answer:

Part A:

y = minutes doing freehand exercises

x = minutes running on the treadmill

Write a pair of linear equations:y + x = 60 (total time at the gym)x = y + 30 (running time is 30 minutes more than freehand time)Part B:

To find the time Jacob spends doing freehand exercises, substitute the value of x from the second equation into the first equation:

y + (y + 30) = 60

2y + 30 = 60

2y = 30

y = 15