System of Linear Equations - Calories burned

pulse225

New member
Stuck trying to figure out a problem using a system of linear equations to solve.
While performing interval training, a person follows a routine of a period of high intensity followed by a period twice as long of low intensity.
During the high intensity, the rate of calories burned is 13 cals/min.
The time per periods is always 1:2.
What is the rate of the lower intensity period to ensure a total of 320 cals burned and how much time per period??

If additional information is needed, you can make it for a total of 10 sets.

pulse225

New member
I'm stuck on the second equation of the following problem,

While performing interval workouts, a person performs a period of high intensity exercise (HI) followed by a period of low intensity (LI).
The ratio of HI to LI is 2:1.
HI burns 13 cals/min.
What is the rate of calorie burn that is required to maintain a total of 320 cals burned and how long is each period.

x = cals/min LI
t = time of each period

13t + x(2t) = 320

I can't figure out the second part.

Subhotosh Khan

Super Moderator
Staff member
I'm stuck on the second equation of the following problem,

While performing interval workouts, a person performs a period of high intensity exercise (HI) followed by a period of low intensity (LI).
The ratio of HI to LI is 2:1.
HI burns 13 cals/min.
What is the rate of calorie burn that is required to maintain a total of 320 cals burned and how long is each period.

x = cals/min LI
t = time of each period

13t + x(2t) = 320

I can't figure out the second part.
Does The ratio of HI to LI is 2:1 mean 13 : x = 2 : 1?

pulse225

New member
Does The ratio of HI to LI is 2:1 mean 13 : x = 2 : 1?
No, I'm sorry, the ratio of time spent in HI to LI is 1:2.

mmm4444bot

Super Moderator
Staff member
It seems to me that there are multiple solutions because the exercise does not tell us how the two calorie-burning rates are related. Alternatively, they could have given us the total minutes spent exercising. Then we could narrow it down to a specific solution.

For examples:

LI rate of 9-1/2 cal/min --> 10 min HI + 20 min LI = 320 calories

LI rate of 6-5/6 cal/min --> 12 min HI + 24 min LI = 320 calories

LI rate of 4-1/6 cal/min --> 15 min HI + 30 min LI = 320 calories

LI rate of 3-1/2 cal/min --> 16 min HI + 32 min LI = 320 calories

LI rate of 1-1/2 cal/min --> 20 min HI + 40 min LI = 320 calories

There are many other possibilities; how can we know which one they're talking about?

If they had included a statement like, "Total exercise time is 36 min", then we could give a specific answer.

If they had included a statement like, "The ratio of HI rate to LI rate is 26:3", then we could give a specific answer.