A 150 -lb person who runs at 6 mph for 1 hr burns about 720...

A 150 -lb person who runs at 6 mph for 1 hr burns about 720 calories. The same person, walking at $4 \mathrm{mph}$ for $90 \mathrm{min}$, burns about 480 calories. (Source: FitSmart, USA Weekend, July $19-21,2002)$ Suppose that a 150 -lb person runs at 6 mph for 75 min. How far would the person have to walk at $4 \mathrm{mph}$ in order to burn the same number of calories used running?

Key Concepts

Proportional Reasoning

This concept involves understanding that if two quantities are directly proportional, scaling one will proportionally scale the other. In exercise scenarios, if a person burns a certain number of calories in one activity for a given duration, the calorie burn for a different activity can be predicted by maintaining the same ratio, assuming linear relationships between time and energy expenditure.

Caloric Burn Rate

The caloric burn rate is a measure of how many calories are expended per unit of time during a specific physical activity. It allows for the comparison and conversion of energy expenditure between different exercises, making it possible to calculate how long or far one needs to engage in an activity to burn a set amount of calories.

Unit Conversion and Dimensional Analysis

This concept involves converting units so that they are consistent throughout a calculation. Common conversions include changing minutes to hours or computing distance using speed and time. Ensuring that units match is essential for accurate calculations when comparing rates of energy expenditure or transit across different activities.

Relationship between Speed, Time, and Distance

This principle states that the distance traveled during an activity is the product of the speed and the time spent performing the activity. In contexts such as walking or running, if the speed is known and the required duration is determined (for instance, based on calorie burn), the overall distance can be easily calculated using the formula: distance = speed × time.

Transcript

00:01 We have some running and walking going on and calories.

00:04 So let's see, we have 6 miles per 150 pound person, 6 miles per hour for an hour is 720 calories.

00:13 And some other information, and let's see what the question is.

00:15 How far? so suppose that 150 pound person runs at this speed for this amount of time.

00:25 How far would the person have to walk at this speed in order to burn the same number of calories as running? so it's like, i don't want to run.

00:34 I want to walk at this speed, but i still want to burn the same amount of calories.

00:37 That's what being asked here.

00:39 So we have to play around with what we're given.

00:41 So let's see, six miles per hour for an hour burns 720 calories.

00:45 So let's tinker with this.

00:46 This means that six miles gives us 720 calories.

00:56 So if we convert this into a useful ratio for us, because we're talking about some distance here.

01:03 Here.

01:08 Let's see.

01:08 This means one mile, if we divide by six, will burn...

01:15 This is running.

01:16 I should say this is running.

01:21 We'll give us 120 calories.

01:25 So basically 120 calories per mile.

01:27 That's what this means.

01:31 And if we're running six miles per hour for 75 minutes, let's see how far we would have ran.

01:39 Six miles per hour.

01:44 Seventy -five is also five quarters of an hour.

01:52 So that would put us at, what is that, seven and a half miles.

02:00 So that means the total calories we would have burned would be, what, this many miles times 120 calories per mile.

02:16 Whoops, a little foreshadowing there.

02:22 Nine hundred.

02:27 So let's look at the running or the walking scenario.

02:35 Let's see, what's our walking stuff here? let's see, four miles per hour for 90 minutes burns 480 calories.

02:43 So four miles...

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