Counting Billy's Coin Combinations & Gabriela's School Trip Time

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Homework Help Overview

The discussion revolves around two distinct problems: one involving counting the arrangements of coins and the other concerning the time taken for Gabriela to bike to school compared to Juan's walking time. The first problem is related to permutations in combinatorics, while the second involves rates and distances in a real-world context.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the arrangement of coins in a square format and question the implications of the problem statement regarding the distances for Gabriela and Juan. There is uncertainty about the assumptions made regarding their living situation and the distances involved.

Discussion Status

Some participants have provided insights into the nature of the first problem, suggesting that it involves permutations and offering hints about how to approach it. The second problem has seen agreement on the assumption that both siblings likely travel the same distance, although this remains an assumption rather than a confirmed fact.

Contextual Notes

Participants note the lack of a visual reference for the "following board" mentioned in the first problem, which may affect understanding. There is also a recognition of the need to clarify the assumptions regarding the distances traveled by Juan and Gabriela.

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Homework Statement


Billy has 1 penny, 1 nickel, 1 dime and 1 quarter. How many different ways can he put his coins in the following board by placing one coin in each cell?

Juan walks to school everyday. His walking speed is 1/15 mile per minute, and it takes him 30 minutes to get to school. His sister Gabriela bikes to school every day. Her biking speed is 1/10 mile per minute. How many minutes does it take Gabriela to get to school?

The Attempt at a Solution


Not sure how to do the first one. The second one I got the answer by multiplying Juan's speed x time to get the distance he traveled. Then with that distance, I divided it by Gabriela's speed to get how long it takes her. But the problem says nothing about the distances being the same, I just don't know
 
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I think you're right for the second question. The question implies the differences are the same because Gabriella and Juan probably live together and go to the same school! It's just an assumption you have to make ;)

For the first question, was there more to the problem statement? It says something about "the following board" but I see no board :)
 
oh, the first problem has a picture of a square divided into four squares, and you place a coin in each one. I don't remember how to do permutations (?) or combinations.
 
See if this helps: you can think of the 4 squares as being just four spaces. So arranging them in square form, you could arrange them _ _ _ _, and it works out the same. Does that make sense?

In this case you have a permutation, because the order that you put the coins down matters. So what do you think you should do? (Hint: how many ways can you fill the first space?)
 
it is rather easy, in the first task you need to multiply 4x3x2x1 then you will have all the possibilities, to next task i would suggest you to do it across , i mean 1/15 -- 30 and below 1/10 -- x , multiply across, and you have a right answer
good luck
 

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