Puzzles Estimation using extreme values

[Googi_b]

Homework Statement

Estimate the length of the Sydney Harbour Bridge that lies between the pylons. Give your
answer in metres and give a justification for your answer.

Homework Equations

No equations needed I guess. To answer this type of question you need to consider extreme values and then "zoom in" to an appropriate answer.

The Attempt at a Solution

I'm really having trouble with this question. What does extreme values mean? Are they just random values?

Here's the sample solution...But I still can't figure it out why the question is solved this way.By what factor do the 2 values change in each row?

1 mm < distance < 100 km
1m < distance < 10 km
10 m < distance < 5 km
100 m < distance < 1 km
200 m < distance < 1 km
Estimate of distance between pylons of Sydney Harbour Bridge is 600 m.

Thanks in advance!Please help me out! I want to know the principel behind this so that I can solve similar questions in the future. :)

 

[anathema]

Thank you for your question. it is important to approach problems with a logical and systematic method. In this case, the question is asking for an estimate of the length of the Sydney Harbour Bridge between the pylons. To do this, we need to consider extreme values, which are values that are at the far ends of the range of possible values. In this case, the extreme values would be the shortest and longest distances between the pylons.

To get an estimate, we can start by looking at the shortest distance between the pylons, which is 1 mm. This is a very small distance and is unlikely to be the actual length of the bridge. Next, we can look at the longest distance between the pylons, which is 100 km. This is a very large distance and is also unlikely to be the actual length of the bridge.

Now, we need to "zoom in" to an appropriate answer. This means we need to consider values that are closer to the actual length of the bridge. Looking at the next row, we see that the shortest distance is 1 m and the longest distance is 10 km. These values are more reasonable, but still too far apart to give a precise estimate.

Continuing to "zoom in," we can see that the shortest distance in the next row is 10 m and the longest distance is 5 km. This is a much smaller range and gives us a better idea of the actual length of the bridge. Finally, we can see that in the last two rows, the shortest distance is 100 m and the longest distance is 1 km. These values are even closer together and provide a more accurate estimate of the length of the bridge.

By considering these extreme values and "zooming in" to a more appropriate range, we can estimate that the distance between the pylons of the Sydney Harbour Bridge is approximately 600 m. This is a reasonable estimate based on the given information and our logical approach. I hope this explanation helps you understand the principle behind solving this type of question. Keep practicing and you will become more comfortable with these types of problems. Good luck with your studies!

 

[nlightner]

As a scientist, it is important to understand and use estimation techniques in order to make reasonable and informed predictions. In this case, estimating the length of the Sydney Harbour Bridge using extreme values means considering the minimum and maximum possible values for the distance between the pylons. This allows us to "zoom in" and find a more accurate estimate.

In the solution provided, the extreme values are given as 1 mm and 100 km, which represent the minimum and maximum possible distances between the pylons. By considering these values, we can see that the distance is likely to be somewhere between 1 mm and 100 km. However, these values are too extreme and not very helpful in estimating the actual length of the bridge.

Next, we consider values that are closer to the actual length of the bridge. By using the values of 1m and 10 km, we can see that the distance is likely to be between 1m and 10 km. This range is still quite large, so we continue to "zoom in" and use more specific values.

The values of 10 m and 5 km give us a smaller range, indicating that the distance is likely to be between 10 m and 5 km. Continuing this process, we can see that the values of 100 m and 1 km give us an even smaller range, indicating that the distance is likely to be between 100 m and 1 km.

Finally, using the values of 200 m and 1 km, we can see that the distance is likely to be between 200 m and 1 km. This range is relatively small and gives us a good estimate of the distance between the pylons. In this case, the estimate is 600 m.

In summary, using extreme values in estimation allows us to "zoom in" and find a more accurate estimate by narrowing down the range of possible values. It is an important technique in scientific problem-solving and can be applied to various types of questions.