The average speed for the entire trip from home to the gift store and back is 15 miles per hour
<em><u>Solution:</u></em>
Given that, Starting at home Michael travel uphill to the gift store for 24 minutes after 10 mph
1 hour = 60 minutes
![24\ minutes = \frac{24}{60}\ hour](https://tex.z-dn.net/?f=24%5C%20minutes%20%3D%20%5Cfrac%7B24%7D%7B60%7D%5C%20hour)
You can travel back home along the same path down hill at a speed of 30 mph
<em><u>The distance is given as:</u></em>
![distance = speed \times time](https://tex.z-dn.net/?f=distance%20%3D%20speed%20%5Ctimes%20time)
<em><u>Uphill distance:</u></em>
![Uphill\ Distance = 10 \times \frac{24}{60} = 4 \text{ miles }](https://tex.z-dn.net/?f=Uphill%5C%20Distance%20%3D%2010%20%5Ctimes%20%5Cfrac%7B24%7D%7B60%7D%20%20%3D%204%20%5Ctext%7B%20miles%20%7D)
The downhill distance will also be same 4 miles at a speed of 30 mph
<em><u>Find the time taken for down trip</u></em>
![time = \frac{4}{30} = 0.133](https://tex.z-dn.net/?f=time%20%3D%20%5Cfrac%7B4%7D%7B30%7D%20%3D%200.133)
Thus, time taken for downtrip = 0.133 hours
![Total\ time\ taken = \frac{24}{60} + 0.133\\\\Total\ time\ taken =0.533\ hours](https://tex.z-dn.net/?f=Total%5C%20time%5C%20taken%20%3D%20%5Cfrac%7B24%7D%7B60%7D%20%2B%200.133%5C%5C%5C%5CTotal%5C%20time%5C%20taken%20%3D0.533%5C%20hours)
Total distance traveled = 4 miles + 4 miles = 8 miles
<em><u>The average speed is given by formula:</u></em>
![\text{Average Speed } = \frac{\text{Total distance traveled}}{\text{Total time taken}}](https://tex.z-dn.net/?f=%5Ctext%7BAverage%20Speed%20%7D%20%3D%20%5Cfrac%7B%5Ctext%7BTotal%20distance%20traveled%7D%7D%7B%5Ctext%7BTotal%20time%20taken%7D%7D)
<em><u>Substituting the values we get,</u></em>
![Average\ speed = \frac{8}{0.533} = 15.009 \approx 15](https://tex.z-dn.net/?f=Average%5C%20speed%20%3D%20%5Cfrac%7B8%7D%7B0.533%7D%20%3D%2015.009%20%5Capprox%2015)
Thus average speed for the entire trip from home to the gift store and back is 15 miles per hour