Distance, Speed, and Time Amanda, Bryce, and Corey enter a...

Name: Problem 71, Chapter 11: Algebra and Trigonometry
Uploaded: 2020-03-13T21:10:30-08:00
Duration: 8 min 13 s
Channel: Sherrie Fenner
Description: Distance, Speed, and Time 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 h 45 min. Amanda comes in second with a time of 2 h 30 min. Bryce finishes last with a time of 3 h. Find the distance (in mi) for each part of the race.

Distance, Speed, and Time 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 h 45 min. Amanda comes in second with a time of 2 h 30 min. Bryce finishes last with a time of 3 h. Find the distance (in mi) for each part of the race.

Distance, Speed, and Time 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 h 45 min. Amanda
comes in second with a time of 2 h 30 min. Bryce finishes
last with a time of 3 h. Find the distance (in mi) for each part
of the race.

Key Concepts

System of Equations

When a problem involves several unknown distances or times across different segments, a system of equations is created from the relationships for each segment. By using the distance-speed-time relationship for each participant or segment and combining them with given total times or distances, one can form simultaneous equations whose solution yields the individual distances or times.

Unit Conversion

In problems where time or speed data are presented in different units, such as hours and minutes, converting all quantities to consistent units is essential. This step prevents errors and ensures that the mathematical relationships, like the distance-speed-time formula, are applied correctly throughout the problem-solving process.

Distance-Speed-Time Relationship

This concept involves understanding the fundamental formula that connects distance, speed, and time, which is expressed as distance = speed × time. In problems involving motion over different segments or activities, this relationship is the starting point to set up equations that model each part of the journey, allowing for computation of unknown quantities when two of the variables are known.

Transcript

00:01 Question 71.

00:06 We have 110 plus 1 .4th y plus 120th z equals 2 .5.

00:24 And then we have 1 over 7 .5x plus 1 .16.

00:34 Y plus 115 z equals 3 and 115 plus plus one -third y plus 140th z equals 1 .75.

01:04 So if i multiply this whole thing by 20, 20 times 110 is 2, is 2, 20 times 1 4th is 5, 20 times 1 20th is 1, and 20 times 2 .5 is 50.

01:30 I'm going to multiply this by 30, and how did i pick those numbers? i looked at my denominators, and i came up with the common denominator.

01:43 So i took 15 and they all don't go into 15, so i doubled that.

01:50 30, 6 goes into 30, 7 .5 and 7 .5 is 15, so that would go into 30.

02:00 So now 30 times 1 over 7 .5, 4, 30 times 1 6 is 5, 30 times 1 .15 is 5, 30 times 115 is 2, and 30 times 3 is 90.

02:25 Here, i have to multiply this by 120.

02:29 That would be my common denominator for all of those.

02:34 And i'm going to put this in red.

02:36 So this would be 8, 40, 3, and 2 .10.

02:50 So i have, let me just rewrite this.

02:53 2, 5, 150, 4, 5, 5, 5.

03:09 298 403 to 10.

03:13 So i'm going to take negative 2 times row 1 and add it to row 2 and put it back into row 2.

03:26 So my row 1 stays the same.

03:32 2, 5, 1.

03:37 So 2 times that, negative 2 times that's going to give me negative 4, negative 10, negative 2, negative 1.

03:54 So when i add negative 4 plus 4, i get 0.

04:01 When i add negative 10 and 5, i get negative 5, negative 3 plus, i'm sorry, negative 2 plus 2 and 0, and negative 100 plus 90 is negative 10.

04:15 Now i'm going to take a negative 4 times row 1 plus row 3 into row 3...

Please give Ace some feedback