Question

Jacob spends 60 minutes in the gym every day doing freehand exercises and running on the treadmill. He spends 30 minutes more running on the treadmill than doing 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). (5 points)

Answer 1

Part B: How much time does Jacob spend on doing freehand exercises? (3 points)

Part C: Is it possible for Jacob to have spent 40 minutes running on the treadmill? Explain your reasoning. (2 points)


THIS IS A TEST! DO NOT GIVE ME THE ANSWER! JUST HELP ME SOLVE IT! THANK YOU!

Answer 2

@Ciarán95

Answer 3

Part A:

To form the pair of linear equations, we need to consider the two sets of information we are given in the question:

"Jacob spends 60 minutes in the gym every day doing freehand exercises AND running on the treadmill."

We know that x = minutes on treadmill and y = minutes doing freehand exercises. The total of these two values, when added together, must equal 60. So, what equation can we write to express this problem?

"He spends 30 minutes more running on the treadmill than doing freehand exercises."

This tells us that the total amount of time spent on the treadmill (x) will be 30 more than y. So, our second equation will be the same as the first, except we can replace y with the term 'y + 30'.

Answer 4

Sorry, that last line should read:

So, our second equation will be the same as the first, except we can replace x with the term 'y + 30'.

Apologies! :)

Answer 5

So y = 30?

Answer 6

What was your first equation?

Answer 7

Part B:

The second equation we have formed will just contain y terms and numbers, so there will be no x terms present. This part of the question asks us to find the number of minutes Jacob spends doing freehand exercises (i.e. what is the value of y?).
So, all we need to do is take our second equation (from part A) and rearrange it to solve for y. I won’t tell you what the answer is, but it isn’t y = 30 anyway!

Answer 8

60 = x + y

Answer 9

Yes, that's right! So for our second equation, we're replacing the 'x' term with 'y + 30', as we're told that he will spend 30 minutes more doing the treadmill (x) than doing exercises (y). What do we get?

Answer 10

30 + y = 60... you said it wasnt 30.. what is it?

Answer 11

You've almost got it, but not exactly. We're trying to replace x with the term 'y + 30', not just 30 on it's own.

We don't know what the value of x is, all we know is that it is 30 more than y.
\[x + y = 60\]
When we plug it in, we should get:
\[(y + 30) + y = 60\]

That should be the answer to part A (the two equations). We then solve this second equation for y to find the answer to part B.

Answer 12

y = 15

Answer 13

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Answer 14

Yes, well done! So, we know now that y = 15. What do you make of part C @OswaldMurphy ? Can he have run for 40 minutes on the treadmill, based on what we know?

Answer 15

Yes since y = 15.

Answer 16

Well, we can actually find out the exact value of x, now that we know y.
\[x + y = 60\]

I will plug in 15 for y:
\[x + 15 = 60\]

So, solving for x, what answer do we get?

Answer 17

@OswaldMurphy Solving for x will tell us the exact amount of time Jacob spends on the treadmill every day.

Answer 18

Oh I see, I thought it would be yes because 1 day he was like, Im working for 55 minutes.
x = 45.

Answer 19

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Answer 20

Yes, you've got it! :) He spends exactly 60 minutes a day at the gym.

It makes sense too. Remember, we were told that he did 30 minutes more of treadmill than freehand exercises, so once we found that y = 15, then x must be 15 + 30 = 45.

And that's it I think....hope that helped you out @OswaldMurphy :D

Answer 21

Yes! Thank you! I got a couple more.

Answer 22

So, just to clarify the answer to C is that x cannot be equal to 40!

Answer 23

Ok, what's your other questions?

Answer 24

I will post it and tag you :D

Answer 25

Ok, cool :)