The Problem:

Trip to Sojo’s Problem of the Week

Juaquin loves to go to Sojourner’s Coffee Shop after getting to school at 6:50 but before classes start each morning. He knows that since, on average it takes Sojo’s 12 minutes to make a breakfast sandwich and he spends another 13 minutes in the shop eating and chatting, he has to walk at an average speed of 1 mph for the fifth of a mile to make it there and back on time for electives (the distance from RMSEL to Sojo’s is ⅕ of a mile, not the round trip).

On Monday, when Joaquin is wearing his Garmin GPS watch, he notices that he walked at an average speed of 1.2 mph on the way to Sojo’s. Then, he bought a sandwich that cost $7, which left his debit account at $53. Assuming he still spends the normal amount of time waiting, eating, and chatting, how fast must he walk to get back on time for his first class?

Tuesday at lunch Joaquin averages 1.2 mph, and then buys a sandwich that costs $6.50. While waiting, he checks his bank statement from his mobile device instead of enjoying being able to practice patience while waiting, which makes him slightly less present and content. Because he got a paycheck 4 days ago, the sandwich charge leaves his bank account at a balance of $109; feeling good, he spends an extra 7 minutes at Sojo’s chatting after his sandwich arrived in average time. How fast must he walk back in order to make it on time?

Because Juaquin makes this round trip frequently and his average speed to and from Sojo’s varies, he wants to find an expression that will help him. Let x be Juaquin’s average speed to Sojo’s. Help him by creating an expression in terms of x that will tell him what his average speed should be on the return trip in order for his average speed for the whole trip to be 1 mph.

Please keep all of your scratch paper that you used in solving this problem. It may take you many attempts (maybe even many failed attempts) before developing a correct answer - all of these attempts are important records of your learning, as mistakes are the key to strengthening synapses in the brain. There’s learning to be done now, go forth with vigor.

The Write-Up:
You will be completing a final write-up for this paper. Please use the format outlined below, making sure to structure your paper appropriately and to format any mathematical equations you use in the correct way (the Google Docs ‘Equation’ feature is quite handy for this).

Problem Statement:
This is where you overview the topic and problem at hand. The problem statement should be clear enough that someone outside the math community would understand the broader scope of the big question you are asking.

Describe your process in tackling the big question at hand. Include examples of practice
problems that you answered on the way to understanding the big question you were trying to answer - you may need to learn how to type mathematical equations during this section. Include descriptions of things you tried that didn’t work or seemed like a waste of time and explain why. Document and describe any type of assistance you get on the problem (discussions with friends and mathematicians, inquiries to Google, or emotional support from dogs or cats along the way) - describe how the assistance helped you. Describe your process with the problem - did you work a little bit every day? Did you have long, frustrating sessions with the problem? Did a breakthrough come to you in a dream or on a jog?

You understand something completely when you can explain it simply. Explain the
solution or dialogue of your final answer as clearly and simply as possible. Use the equation feature in Google Docs and make the logic clear and easy to follow. Use diagrams if appropriate!

Invent some extensions, variations, or ongoing questions for the problem. Where will this
work take us in the future, what is another example problem that could use this same understanding, and what questions would we still like to answer?

State not only what you learned from this problem, but what you learned about yourself as a student of the world. Analyze your habits of study - did you become frustrated? What did you do about it? What problem-solving techniques did you use in answering the big question and where did your bursts of creativity and enlightenment come? Did they come while hard at work on the problem, or elsewhere? Assign yourself a grade for the process you used in the course of answering this big question.

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These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

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