Respuesta :
Answer:
[tex]\text{Average speed}=\frac{12\text{ miles}}{\text{ Hour}}[/tex]
Step-by-step explanation:
We have been given that Luis traveled uphill to the hardware store for 30 minutes at just 8 mph.
Let us find distance traveled by Luis using distance formula.
[tex]\text{Distance}=\text{Speed}\times \text{Time}[/tex]
30 minutes are equal to 0.5 hour or 1/2 hour.
[tex]\text{Distance}=8\frac{\text{ Miles}}{\text{hour}}\times \text{0.5 hour}[/tex]
[tex]\text{Distance}=8\text{ Miles}\times0.5[/tex]
[tex]\text{Distance}=4\text{ Miles}[/tex]
[tex]\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}[/tex]
Let us find time taken while traveling 4 miles at a rate of 24 mph.
[tex]\text{Time}=\frac{\text{4 miles}}{\frac{\text{24 miles}}{\text{hour}}}[/tex]
[tex]\text{Time}=\frac{\text{4 miles}}{\text{24 miles}}\times \text{hour}[/tex]
[tex]\text{Time}=\frac{1}{6}\times \text{hour}[/tex]
[tex]\text{Time}=10\text{ Minutes}[/tex]
[tex]\text{Average speed}=\frac{\text{4 miles }+\text{ 4 miles}}{\text{30 minutes}+\text{10 minutes}}[/tex]
[tex]\text{Average speed}=\frac{\text{8 miles}}{\text{40 minutes}}[/tex]
[tex]\text{Average speed}=\frac{\text{8 miles}}{\text{40 minutes }\times \frac{1\text{ Hour}}{\text{60 minutes}}}[/tex]
[tex]\text{Average speed}=\frac{\text{8 miles}}{\frac{2}{3}\text{ Hour}}[/tex]
[tex]\text{Average speed}=\frac{8\times 3\text{ miles}}{2\text{ Hour}}[/tex]
[tex]\text{Average speed}=\frac{12\text{ miles}}{\text{ Hour}}[/tex]
Therefore, the average speed is 12 miles per hour.
