- #1
brinlin
- 12
- 0
MHB Solve System of Equations Related to Race Speeds
- Thread starter brinlin
- Start date
Click For Summary
SUMMARY
The discussion focuses on solving a system of equations related to race speeds, specifically for a scenario involving distances run, swum, and cycled by an athlete named Amanda. The retired math professor outlines the process of formulating the equation based on Amanda's velocities: running at 10 mi/hr, swimming at 4 mi/hr, and cycling at 20 mi/hr. The total time taken by Amanda is given as 2.5 hours, leading to the equation x/10 + y/4 + z/20 = 2.5, which simplifies to 2x + 5y + z = 50 when multiplied by 20. The professor emphasizes the importance of showing work in homework to ensure understanding and success in tests.
PREREQUISITES- Understanding of basic algebraic equations
- Familiarity with velocity and time calculations
- Knowledge of unit conversions (e.g., hours to minutes)
- Ability to manipulate fractions and simplify equations
- Practice solving systems of equations using different scenarios
- Learn about unit conversions in physics problems
- Explore the concept of velocity and its applications in real-world problems
- Study methods for verifying solutions in algebraic equations
Students in mathematics courses, educators teaching algebra, and anyone interested in applying mathematical concepts to real-life scenarios involving speed and distance calculations.
- #2
HOI
- 921
- 2
You seem to be under the impression that this is a site that will do your homework for you. It isn't! We don't know you and we don't dislike you enough to want you to fail this course. We will be happy to help you if you show enough of your own work that we can see what help you need.
The whole point of homework is for YOU to practice so you can pass the tests! I hope you want to pass the tests!
[I myself am a retired math professor. I once had a student who turned in perfect homework then failed every test. He complained bitterly when he received an "F" for the course. I have no idea who did his homework for him (he was a fraternity member if anyone thinks that is relevant) but clearly he didn't. They did him no favors!]
The whole point of homework is for YOU to practice so you can pass the tests! I hope you want to pass the tests!
[I myself am a retired math professor. I once had a student who turned in perfect homework then failed every test. He complained bitterly when he received an "F" for the course. I have no idea who did his homework for him (he was a fraternity member if anyone thinks that is relevant) but clearly he didn't. They did him no favors!]
- #3
HOI
- 921
- 2
I'll help you get started. Let the distance each has to run be "x", the distance each has to swim "y", and the distance each has to cycle "z", all in miles, of course.
Velocity has units of mi/hr because it is "distance (mi.) divided by time (hr.)", v= d/t. Multiplying on both sides by t, vt= d. Dividing on both sides by v, t= d/v. I did that because this problem tells us velocities and I have assigned labels to the distances. I have those together on the right side of the equation.
Look at Amanda only, she ran a distance x miles at 10 mi/hr so took x/10 hours. She swam a distance y miles at 4 mi/hr so took y/4 hours. She cycled a distance z miles at 20 mi/hr so took z/20 hr. She took a total x/10+ y/4+ z/20 hours. The problem tells us she took 2 hours and 30 minutes which is 2.5 hours.
The equation is x/10+ y/4+ z/20= 2.5. If you don't like fractions (I don't!) multiply both sides by 20: 2x+ 5y+ z= 50.
Now you finish!
Velocity has units of mi/hr because it is "distance (mi.) divided by time (hr.)", v= d/t. Multiplying on both sides by t, vt= d. Dividing on both sides by v, t= d/v. I did that because this problem tells us velocities and I have assigned labels to the distances. I have those together on the right side of the equation.
Look at Amanda only, she ran a distance x miles at 10 mi/hr so took x/10 hours. She swam a distance y miles at 4 mi/hr so took y/4 hours. She cycled a distance z miles at 20 mi/hr so took z/20 hr. She took a total x/10+ y/4+ z/20 hours. The problem tells us she took 2 hours and 30 minutes which is 2.5 hours.
The equation is x/10+ y/4+ z/20= 2.5. If you don't like fractions (I don't!) multiply both sides by 20: 2x+ 5y+ z= 50.
Now you finish!
Similar threads
- · Replies 7 ·
- · Replies 1 ·
- · Replies 9 ·
- · Replies 5 ·
- · Replies 2 ·
- · Replies 10 ·
- · Replies 10 ·
- · Replies 1 ·
- · Replies 1 ·
- · Replies 5 ·