Sure, let's solve this step-by-step:
1. Identify given data:
We are given the following data points:
- 2 kilometers takes 3 minutes
- 1 kilometer takes [tex]\(1 \frac{1}{2}\)[/tex] (or 1.5) minutes
- 5 kilometers takes [tex]\(7 \frac{1}{2}\)[/tex] (or 7.5) minutes
2. Calculate average speed for each distance:
- For 2 kilometers:
[tex]\[
\text{Speed for 2 km} = \frac{3 \text{ minutes}}{2 \text{ km}} = 1.5 \text{ minutes per kilometer}
\][/tex]
- For 1 kilometer:
[tex]\[
\text{Speed for 1 km} = \frac{1.5 \text{ minutes}}{1 \text{ km}} = 1.5 \text{ minutes per kilometer}
\][/tex]
- For 5 kilometers:
[tex]\[
\text{Speed for 5 km} = \frac{7.5 \text{ minutes}}{5 \text{ km}} = 1.5 \text{ minutes per kilometer}
\][/tex]
3. Determine the average speed:
Since the speeds for each segment are the same:
[tex]\[
\text{Average speed} = \frac{1.5 + 1.5 + 1.5}{3} = 1.5 \text{ minutes per kilometer}
\][/tex]
4. Estimate the time for 60 kilometers:
Using the consistent average speed:
[tex]\[
\text{Time for 60 km} = 60 \text{ km} \times 1.5 \text{ minutes per kilometer} = 90 \text{ minutes}
\][/tex]
5. Conclusion:
Based on the calculations, the time needed to travel 60 kilometers is 90 minutes.
Therefore, the completed table looks like this:
\begin{tabular}{|c|c|}
\hline Kilometers & Minutes \\
\hline 2 & 3 \\
\hline 1 & [tex]$1 \frac{1}{2}$[/tex] \\
\hline 5 & [tex]$7 \frac{1}{2}$[/tex] \\
\hline 60 & 90 \\
\hline
\end{tabular}
