Amanda, Bryce, and Corey enter a race in which they have to...

Amanda, Bryce, and Corey enter a race in which they have to run, swim, and cycle over a marked course. Their average speeds are given in the table. Corey finishes first with a total time of 1 hr 12 min. Amanda comes in second with a time of 1 hr 51 min. Bryce finishes last with a time of 2 hr 18 min. Find the distance (in miles) for each part of the race. running mi swimming mi cycling mi Average speed (mi/h) Running Swimming Cycling Amanda 10 4 20 Bryce 7 1/2 6 15 Corey 15 3 40

Transcript

00:01 Okay, we need to find the distance for each part of this race.

00:05 That includes running, swimming, and cycling.

00:08 And we're given this table with the speeds of these three participants for the different parts of the race in miles per hour.

00:18 Then we're also given their total time, so i'll just add that to the table.

00:24 Amanda's total time was 1 hour and 51 minutes.

00:31 Bryce's total time was 2 hours and 18 minutes, and cory's total time was 1 hour and 12 minutes.

00:47 Okay, so we're trying to find the distance for each part of the race, so that's what we want our variable to be, is those distances.

00:57 So let's start with that.

00:59 Let's say r is going to be the run distance.

01:08 S is going to be the swim distance.

01:16 And c will be the cycle distance.

01:26 Okay, so our variables are distances.

01:28 And we're given these rates for each participant and then ultimately they get a total time.

01:40 So what if we could find the time for each of their legs, running, swimming and cycling, and then add those times up to get the total time.

01:52 So remember distance equals rate times time.

01:59 So if we wanna find the time for each event, we got to divide both sides by r.

02:08 So that tells us that t equals the distance divided by the rate.

02:16 So what would our equation look like? well, let's take amanda's run time.

02:25 It's the distance, which we've given a variable r, divided by her rate, which was 10.

02:34 So that represents her run time.

02:36 How about her swim time? well, it's going to be s, the swim distance, divided by her swim rate, which was 4 miles per hour.

02:52 And then finally, her cycling time would be the cycling distance, which we've given a variable c, divided by the cycling rate, which is 20.

03:06 So we're taking distances and dividing them by rates in miles per hour.

03:13 So that means our answers will be in miles and our time will be in hours.

03:21 So if we add these up, we'll get the total number of hours for amanda, which was, we'll call it 1 and 51 sixtieths of an hour...

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