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# Ernie Exercising Efficiently

## Question

Excess Exercise Ernie can do 20 pullups, or 30 situps, or 40 pushups, in one minute. Doing one pull-up burns 1.5 calories; one sit-up burns 1.8 cal; a push-up burns 1.2 cal. Ernie is too 'pressed' for time; you need to design him two Efficient Exercise Efforts:
(i) Panic Workout: Lasts seven minutes, burns exactly 300 calories, with a total of 200 reps,
(ii) Full Session: At least 30 min, burning at least 1200 calories, with as few reps as possible.
Each workout must contain at least one rep(etition) of each exercise. State how many reps of each type, and total reps, for each workout.

## 5 answers to this question

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i think 726 reps must do. Start with one push up. Then 375 push ups and 350 pull ups.

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1. Reps: p + s + h = 200
2. Calories: 15p + 18s + 12h = 3000
3. Time: p/20 + s/30 + h/40 = 7

From which p = 56; s = 72; h = 72.

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To meet the time and calorie requirement for a single type of exercise requires:

800 pullups or

900 situps or

1200 pushups.

I'm just guessing then, that the fewest reps would result from maximizing the pullup count.

The remaining 1197 cal would be expended by 798 pullups.

The workout would last about 40 minutes.

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There are at least two ways to burn 1200 calories in 30 minutes with 727 reps.

1. 358 pullups (537 calories), 368 situps (662,4 calories), 1 pushup (1,2 calories) - in total it takes 30 minutes and a bit less than 12 seconds
or
2. 359 pullups (538,5 calories), 367 situps (660,6 calories), 1 pushup (1,2calories) - 30 minutes and a bit less than 13 seconds.

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We are still missing the most optimal solution for (ii).

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