Question

part b
how can you use estimation to show that the answer to part a is reasonable?
show hints
10\frac{4}{5} seconds is about 10 seconds, which is about \frac{1}{6} of an hour. that means that in 1 hour, the train travels about 6 miles. the speed is about 6 miles per hour. the answer is close to the estimate, so it is reasonable.
10\frac{4}{5} seconds is about 10 seconds, which is about \frac{1}{10} of an hour. that means that in 1 hour, the train travels about 10 miles. the speed of the train is about 10 miles per hour. the answer is close to the estimate, so it is reasonable.
10\frac{4}{5} seconds is about 10 seconds, which is about \frac{1}{6} of a minute. there are 60 minutes in an hour, so the train travels 1 mile in about \frac{1}{360} hour. that means in 1 hour, the train travels 360 miles or 360 miles per hours. the answer is close to the estimate, so it is reasonable.
10\frac{4}{5} seconds is about 10 seconds, which is about \frac{1}{10} of a minute. that means that in 1 minute, the train travels about 10 miles. because there are 60 minutes in an hour, the train travels about
600 miles, or 600 miles per hour. the answer is close to the estimate, so it is reasonable.

Explanation:

Step1: Analyze the time - unit conversion

We know that \(1\) hour \( = 3600\) seconds. \(10\frac{4}{5}=10.8\) seconds.

Step2: Estimate the number of intervals

We want to find out how many times \(10.8\) seconds fits into \(3600\) seconds. \(\frac{3600}{10.8}\approx\frac{3600}{10} = 360\) (using estimation).

Step3: Relate to speed

If we assume that in \(10.8\) seconds (approx \(10\) seconds for estimation) the train travels a certain distance. If we consider the number of \(10\) - second intervals in an hour (\(3600\) seconds), and if we assume a simple proportional relationship (for estimation purposes). For example, if we assume that in \(10\) seconds the train travels a distance \(d\), then in \(3600\) seconds (1 hour) it travels \(360d\). If we assume \(d = 1\) mile (a very rough assumption for estimation), then the speed is \(360\) miles per hour.

Answer:

The option “\(10\frac{4}{5}\) seconds is about \(10\) seconds, which is about \(\frac{1}{360}\) of an hour. The answer is close to the estimate, so it is reasonable.” is correct.