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

In summary, Juan walks to school everyday and it takes him 30 minutes. Gabriela bike to school everyday and it takes her 10 minutes. Therefore, it takes Juan x minutes and Gabriela y minutes to get to school.
  • #1
johnnyies
93
0

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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  • #2
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 :)
 
  • #3
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.
 
  • #4
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?)
 
  • #5
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
 

1. How do you count the number of coin combinations for Billy?

In order to count the number of coin combinations for Billy, you would need to know the types of coins he has and their respective values. Then, you would use a combination formula (e.g. nCr) to calculate all the possible combinations. For example, if Billy has 4 different types of coins, you would calculate the number of combinations for each type and then multiply them together to get the total number of combinations.

2. What is the importance of counting coin combinations for Billy?

The importance of counting coin combinations for Billy is to determine the total value of his coins. This can be helpful for budgeting, tracking expenses, or simply understanding how much money he has.

3. How do you calculate the time it takes for Gabriela's school trip?

To calculate the time it takes for Gabriela's school trip, you would need to know the distance she is traveling and the speed at which she is traveling. Then, you can use the formula time = distance/speed to determine the total time it takes for her trip.

4. What factors can affect the time it takes for Gabriela's school trip?

The time it takes for Gabriela's school trip can be affected by various factors such as traffic, road conditions, speed limits, and any stops or detours along the way. Additionally, the mode of transportation used (e.g. car, bus, train) can also impact the total travel time.

5. How can counting coin combinations and calculating Gabriela's school trip time be applied in real-life situations?

The skills of counting coin combinations and calculating travel time can be applied in various real-life situations. For example, counting coin combinations can be useful for managing personal finances or working in a retail or banking setting. Calculating travel time can be helpful for planning trips, estimating arrival times, or determining the most efficient route to take. These skills can also be applied in fields such as logistics, transportation, and project management.

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