Alright, let's analyze the situation step by step to identify and correct Venetta's mistake.
1. Understanding the Conversion Factor:
- Venetta knows that 1 mile (mi) is approximately equal to 1.6 kilometers (km). In conversion terms, [tex]\(1 \text{ mi} \approx 1.6 \text{ km}\)[/tex].
2. Correct Conversion Method:
- To convert from miles per hour (mi/h) to kilometers per hour (km/h), we should multiply the speed value in miles per hour by the conversion factor [tex]\(1 \text{ mi} = 1.6 \text{ km}\)[/tex].
3. Correct Calculation:
- For converting 5 miles per hour (mi/h) to kilometers per hour (km/h), the correct operation:
[tex]\[
5 \text{ mi/h} \times 1.6 \text{ km/mi} = 8 \text{ km/h}
\][/tex]
- So, the correct speed in km/h is 8 km/h.
4. Venetta's Mistake:
- Venetta multiplies 5 mi/h by [tex]\(\frac{1 \text{ mi}}{1.6 \text{ km}}\)[/tex], which is incorrect. Let's perform her calculation:
[tex]\[
5 \text{ mi/h} \times \frac{1 \text{ mi}}{1.6 \text{ km}} = \frac{5}{1.6} \text{ km/h} \approx 3.125 \text{ km/h}
\][/tex]
- So, her incorrect speed conversion is approximately 3.125 km/h.
5. Identifying the Error:
- To find the error Venetta made, we subtract her incorrect result from the correct result:
[tex]\[
\text{Error} = 8 \text{ km/h} - 3.125 \text{ km/h} = 4.875 \text{ km/h}
\][/tex]
6. Conclusion:
- Venetta made an error by dividing instead of multiplying by the conversion factor. As a result, her converted speed was 4.875 km/h less than it should have been.
Thus, Venetta's error in conversion led to an incorrect speed of 3.125 km/h instead of the correct speed of 8.0 km/h, resulting in an error of 4.875 km/h.
