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You have 40 minutes to exercise at the gym, and you want to burn 300 calories total using both machines. How much time should you spend on each machine?(one burns 8cal per min, the other burns 6cal per min) please explain how you got it



Verified Answer :

annaq14

first I did 300 divided by 2 because there are two machines. I got 150 calories each. then I did there first machine and divided 150 by 8 to get 18.75min. then I took the second machine and did the same thing, did 150 divided by 6 and got 25. then I added18.75 and 25 and got 43, but I need 40 min. so I subtracted 3 from the mon. of the second machine and got 22 instead of 25.

the first machine spend 18.75 min. and the second machine spend 22min.

boffeemadrid

The number of minutes spent on each machine is required.

The time spent on one machine will be 30 minutes and the other machine will be 10 minutes.

Let the number of minutes spent on one machine be \(x\)

and number of minutes spent on the other machine be \(y\)

Total time spent is 40 minutes

\(x+y=40\)

Calories burnt in one machine 8 cal per min

Calories burnt in other machine is 6 cal per min

Total calories to be burnt is 300 calories

\(8x+6y=300\)

The equations are

\(x+y=40\)   \(\times 8\)

\(8x+6y=300\)

\(8x+8y=320\)

\(8x+6y=300\)

Subtracting the equations

\(2y=20\\\Rightarrow y=\dfrac{20}{2}\\\Rightarrow y=10\)

\(x+y=40\\\Rightarrow x=40-y=40-10\\\Rightarrow x=30\)

The time spent on one machine will be 30 minutes and the other machine will be 10 minutes.

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