Lucy is choosing between two exercise routines in routine 1...

Lucy is choosing between two exercise routines. In Routine #1, she does only running, burning 10.5 calories per minute. In Routine #2, she burns 22 calories walking. She then runs at a rate that burns 8.3 calories per minute. For what amounts of time spent running will Routine #1 burn more calories than Routine #2? Use t for the number of minutes spent running, and solve your inequality for t.

Transcript

00:01 Alright so the best thing to do for this one is we're working on two different routines of exercise trying to decide which one is better.

00:10 So i called routine one where she runs, she burns 10 .5 calories per minute.

00:17 So our equation, the calories is equal to 10 .5 times t, times the time.

00:27 For routine number two, the calories, it's 22 from walking plus 8 .3 times the time.

00:40 Now okay so it's kind of weird because there's an amount of time, she has to walk for a certain amount of time so it doesn't necessarily start at zero.

00:57 I'm going to pause the video because i want to double check the problem.

01:00 But t doesn't start at zero, she doesn't just magically burn 22 calories then start the time.

01:07 So it has to start, so i'm going to double check the problem, make sure i'm doing it correctly.

01:10 Give me a second.

01:12 Alright i just double checked the problem.

01:13 So t is the amount of time spent running.

01:16 So we're not counting her walking time.

01:19 So if we graph these, so that makes things a little bit easier.

01:22 So when we graph 10 .5 t, so this is my time down here, this is the calories burned here, this is what my graph looks like for routine one.

01:46 It's a slope, it's a line, it has a slope of 10 .5.

01:51 The slope starts at zero, zero, she doesn't run, she doesn't burn anything.

01:55 Okay for routine two we have to start up here at 22.

02:01 Now their slope is only 8 .3, so it's not as steep.

02:09 And that's what that graph looks like.

02:10 I'm just kind of estimating it.

02:12 So this point right here where they hit, that's going to be the time where all the, you know, before that time, that's how long it basically takes her to get to burn 22 calories running.

02:29 So, you know, she burns 22 calories walking, but we're just looking at the time she runs.

02:35 So to find that you set these equal to each other.

02:39 Go 10 .5 t is going to equal 22 plus 8 .3 t.

02:52 And when you subtract the 8 .3 t, we get 2 .2 t equals 22, divide by 2 .2, and t comes out to equal 10.

03:12 Okay, so if she just runs for 10 minutes, if she's only going to run for 10 minutes, then it doesn't matter which routine she uses...

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