The average speed for the entire trip from home to the gift store and back is 15 miles per hour
Solution:
Given that, Starting at home Michael travel uphill to the gift store for 24 minutes after 10 mph
1 hour = 60 minutes
[tex]24\ minutes = \frac{24}{60}\ hour[/tex]
You can travel back home along the same path down hill at a speed of 30 mph
The distance is given as:
[tex]distance = speed \times time[/tex]
Uphill distance:
[tex]Uphill\ Distance = 10 \times \frac{24}{60} = 4 \text{ miles }[/tex]
The downhill distance will also be same 4 miles at a speed of 30 mph
Find the time taken for down trip
[tex]time = \frac{4}{30} = 0.133[/tex]
Thus, time taken for downtrip = 0.133 hours
[tex]Total\ time\ taken = \frac{24}{60} + 0.133\\\\Total\ time\ taken =0.533\ hours[/tex]
Total distance traveled = 4 miles + 4 miles = 8 miles
The average speed is given by formula:
[tex]\text{Average Speed } = \frac{\text{Total distance traveled}}{\text{Total time taken}}[/tex]
Substituting the values we get,
[tex]Average\ speed = \frac{8}{0.533} = 15.009 \approx 15[/tex]
Thus average speed for the entire trip from home to the gift store and back is 15 miles per hour
