MHB Solve System of Equations Related to Race Speeds

AI Thread Summary
The discussion emphasizes the importance of individual effort in solving homework problems, particularly in mathematics. A retired math professor shares an anecdote about a student who excelled in homework but failed tests, highlighting the necessity of understanding the material. The professor provides a starting point for solving a system of equations related to race speeds, defining variables for running, swimming, and cycling distances. An equation is derived based on Amanda's total time for the race, which is x/10 + y/4 + z/20 = 2.5, and simplified to 2x + 5y + z = 50. The thread encourages students to engage with the problem and complete the solution independently.
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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!]
 
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!
 

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