## Apply linear algebra using extended abstract thinking, Algebra

Assignment Help:

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.

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