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Learning Math Home
Patterns, Functions, and Algebra
Session 5 Part A Part B Part C Part D Part E Homework
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Session 5 Materials:

Session 5:

Problem H1


In the Achilles and the tortoise problems in Part C, Achilles runs at a constant rate of 9 miles per hour, and the tortoise moves at 1 mile per hour. Suppose that the speeds of Achilles and the tortoise are unchanged but Achilles catches up to the tortoise in 1 1/2 hours. How much of a head start did the tortoise get?

Stop!  Do the above problem before you proceed.  Use the tip text to help you solve the problem if you get stuck.
Using a spreadsheet can help solve this problem.   Close Tip


Problem H2


The tortoise has taken some "turtle speedup potion" and can now walk at 2 miles per hour. If Achilles still runs at 9 miles per hour and catches up to the tortoise in 3 hours, how much of a head start did the tortoise get?


Problem H3


Here's a trick that master carpenter Norm Abram might use when building supports for roofs. He knows he'll need evenly spaced supports along the roof. He carefully measures what length he needs for the 1st one, and finds that it's 12 feet. Then he measures what he'll need for the 2nd, and finds it is 9 feet. He calls to his assistant: "Don't measure the others, just make them 6 and 3 feet long!" Why does Norm's trick work?

roof image


Problem H4


You've worked with undoing functions. Take a moment to think about undoing a linear function. If given the formula d = 3t + 2 for distance traveled in terms of time, what would you do to express time in terms of distance? When undoing a linear function, will the result always be a new function? If so, will the new function always be a linear function?

Next > Session 6: Solving Equations

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