Q&A: Understanding Part C of a Round Trip Problem

  • MHB
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In summary, the answer key states that there are 14 possible ways to reach point C in part c of the question. However, depending on which roads are used, the number of ways to return home can vary between 10 and 13. For example, if R8 is taken to get to C, there are 13 ways to return home (excluding R8). However, if R1R5 is taken, there are only 10 ways to return home (excluding R1 and R5). The reasoning behind this is that if Linda takes R1R5 to get to C, she cannot take the return trip of R5R1, but all other trips are allowed. This may be the source of confusion.
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find_the_fun
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I don't understand the answer for part c of the following question

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The answer key gives 14x13 as the solution to part c. I understand there are 14 ways to get to point C but depending on which road can no longer be used, there is anywhere between 10 and 13 ways to return home. For example, say R8 was taken to get to C. Then there are 14-1 ways to make the return trip (just don't use R8). However, if R1R5 is used then we can't use either R1 (so now there are 3x3+2=11 ways to make the trip) or R5 (so now there are 2x4+2=10 ways to make the trip). What is wrong with my reasoning?
 

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As I understand the problem statement in c), if Linda takes R1R5 to get from A to C, there is a single trip she is not allowed to take back: R5R1. All other trips are allowed.
 

FAQ: Q&A: Understanding Part C of a Round Trip Problem

What is Part C of a Round Trip Problem?

Part C of a Round Trip Problem refers to the third and final step in solving a round trip problem. It involves finding the total distance traveled and the average speed of the entire trip.

How is Part C different from Parts A and B of a Round Trip Problem?

Parts A and B of a Round Trip Problem involve finding the distance and average speed of individual legs of a trip. Part C, on the other hand, focuses on the overall trip and combines the distances and speeds of each leg to find the total distance and average speed.

Why is it important to understand Part C of a Round Trip Problem?

Understanding Part C of a Round Trip Problem allows you to accurately calculate the total distance and average speed of a trip, which is crucial for planning travel time and expenses. It also helps you identify any discrepancies in your calculations and make corrections if needed.

What information do I need to solve Part C of a Round Trip Problem?

To solve Part C of a Round Trip Problem, you will need the distances and average speeds of each leg of the trip. You may also need the time of each leg, depending on the problem. It is important to have accurate and consistent units for all of these values.

Can you provide an example of solving Part C of a Round Trip Problem?

Sure, here is an example: A car travels 100 miles at an average speed of 50 miles per hour. It then travels back the same distance at an average speed of 60 miles per hour. To find the total distance, we add 100 miles (outward trip) + 100 miles (return trip) = 200 miles. To find the average speed, we calculate the total time: 100 miles / 50 mph = 2 hours (outward trip) and 100 miles / 60 mph = 1.67 hours (return trip). Then, we find the total time: 2 hours + 1.67 hours = 3.67 hours. Finally, we divide the total distance by the total time: 200 miles / 3.67 hours = 54.47 mph. So, the total distance is 200 miles and the average speed is 54.47 mph.

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