Answer:
Average speed = [tex]\frac{(x+y)}{2}[/tex] miles per hour
Step-by-step explanation:
Formula to calculate the average speed of an object is,
Average speed = [tex]\frac{\text{Total distance covered}}{\text{Time taken to cover this distance}}[/tex]
If I travel with the speed of x mph for t hours,
Total distance covered = Speed × Time
= [tex]x\times t[/tex]
= [tex]xt[/tex] miles
Similarly, if I travel with the speed y mph for t hours,
Total distance covered = [tex]yt[/tex] miles
Total distance covered by me = [tex](xt+yt)[/tex] miles
Total time taken to cover this distance = [tex]t+t[/tex]
= [tex]2t[/tex] hours
Therefore, expression for the average speed will be,
Average speed = [tex]\frac{xt+yt}{2t}[/tex]
= [tex]\frac{(x+y)t}{2t}[/tex]
= [tex]\frac{x+y}{2}[/tex] miles per hour
