We know Distance formula is Distance = speed * time
[tex]time = \frac{distance}{speed}[/tex]
Let, the distance Omar traveled = d and speed is 10 miles per hour
Time taken t for the first trip [tex]t = \frac{d}{10}[/tex]
Let, the distance Omar traveled = d and speed is 30 miles per hour
Time taken t for the return trip [tex]t = \frac{d}{30}[/tex]
Total time taken = [tex]\frac{d}{10} + \frac{d}{30} = \frac{3d+d}{30} = \frac{4d}{30}[/tex]
Now, [tex]Average \ speed = \frac{total \ distance}{total \ time \ taken}[/tex]
Total distance = d+d= 2d
Average speed = [tex]\frac{2d}{\frac{4d}{30}}[/tex] = [tex]2d * \frac{30}{4d} = 15[/tex]
His average speed for the entire trip from home to the gift store and back is
15 miles per hour
