High School

charlie had 80 minutes to spend at the gym, where they will run, swim, and ride a bicycle. running uses 11 calories per minute; swimming uses 8 calories per minute; and bicycling uses 2 calories per minute. they run twice as long as they ride the bike. how long should they participate in each of these activities in order to use 640 calories?

Answer :

Charlie should ride the bike for 20 minutes, run for 40 minutes, and swim for 20 minutes in order to burn 640 calories.

Let's call the time Charlie spends riding the bike "x".

Since Charlie runs twice as long as they ride the bike, they will spend 2x time running

The total time Charlie spends exercising is 80 minutes, so we can write an equation

x + 2x + y = 80

where "y" is the time spent swimming.

We also know that the number of calories burned during each activity is given by

Calories burned running = 11 × 2x = 22x

Calories burned swimming = 8y

Calories burned riding bike = 2x

To burn 640 calories in total, we can write another equation

22x + 8y + 2x = 640

Simplifying this equation, we get

24x + 8y = 640

Dividing both sides by 8, we get

3x + y = 80

Now we have two equations with two variables

x + 2x + y = 80

3x + y = 80

Solving for y in terms of x in the second equation

y = 80 - 3x

Substituting this into the first equation

x + 2x + (80 - 3x) = 80

Simplifying

x = 20

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