# Thread: Linear Algebra troubles, please help me? :(

1. ## Linear Algebra troubles, please help me? :(

Hey guys, so my homework are these questions and I think I have the first 3 sussed out in my head, but the criteria requires that I show my workings out by "applying linear algebra using extended abstract thinking in solving problems". None of that makes sense to me and therefore I'm unable to understand anything beyond question 3. If any of you are able to work out the answers to these questions but also show how to get those answers, it would be a huge help to me. I feel I really need to understand these questions and how to answer them using the method/s of the criteria.

INTRO:
Three friends have been training for the Lesley Marathon. The distance of the race around Lake Lesley is 42km (to the nearest kilometre). You can use this distance in your calculations.

HARRY:
Harry is going to enter as a walker. Walkers start at 8.00am. He hopes to walk at a steady pace and complete the 42km distance in seven hours.

AMANDA:
Amanda has been training over long distances at a steady pace of one kilometre every five minutes. Amanda plans to maintain this pace throughout the race. She started at the official time for runners, 10.00am.

FRANK:
Frank plans to run at a steady speed of 14km per hour. Unfortunately Frank started 30 minutes late at 10.30am.

QUESTION 1) if the three friends follow their respective strategies, show their progress through the race on the same graph. Find the equations of their distance covered (d) at any time (t) in hours after 8am.

QUESTION 2) Use your graph and/or equations to describe the race details for each of the three friends. You need to:
a) Calculate how long each person took to complete the race
b) Give details on when and where they will pass each other.

QUESTION 3) How far was Frank behind Amanda, when Amanda reached the halfway point?

QUESTION 4) in the race, Harry was going well for his first four hours and was on target for his intended time, but developed a cramp in his legs and needed to rest for 18 minutes. By what percentage will he need to increase his walking speed for the rest of the race if he is still going to complete the marathon in seven hours?

QUESTION 5) Frank wants to improve his net time by six minutes next year. He will try a different strategy of running for the first two hours at a certain speed and then completing the rest of the race at a rate of 2 kilometres per hour faster than his original speed. If he is to succeed, at what speed will he need to run for the first two hours of next year's Lesley Marathon?

QUESTION 6) The actual distance is 42.2 kilometres (1 d.p.). Explain clearly and in detail how this would affect your calculations of each of the three competitors actual finishing times and places.

QUESTION 7) On the way home the next day the three of them decide to buy some chicken and chips. A piece of chicken costs $2.50 and a scoop of chips costs$2.00. They only have \$20 to spend between them. They want at least one chicken and at least two scoops of chips between them. List the three inequalities involving the chicken and chips purchase and list the possible purchases they could make.

Thank you to everyone who helps me out! I appreciate it.

2. ## Re: Linear Algebra troubles, please help me? :(

We can't answer homework problems directly. Show us what you have been able to do for 1 - 3 for now. We can give some little advice on the rest, but bear in mind that you need to do most/all of the work on these.

-Dan

3. ## Re: Linear Algebra troubles, please help me? :(

While not claiming to be particularly Godlike, we help those who help themselves.

From the information given you should be able to calculate the speed, the time taken to complete the race, and the hours started and ended for each person. From that you will be able to answer all the questions.

(The graphs will be straight lines.)