Answer:45 mi/h
Step-by-step explanation:
Recall: Speed = distance / time
Let the time taken for the morning journey be [tex]t_{1}[/tex] and the time taken for the afternoon journey be [tex]t_{1}[/tex] ,and the distance covered be d
that means for the first journey,
30 = [tex]\frac{d}{t_{1}}[/tex]
d = 30 [tex]t_{1}[/tex]
Also for the afternoon journey,
d = 60 [tex]t_{2}[/tex]
Equating the two , since the same distance is being covered , we have
30 [tex]t_{1}[/tex] = 60 [tex]t_{2}[/tex]
that is
[tex]t_{1}[/tex] = [tex]\frac{60t_{2}}{30}[/tex]
[tex]t_{1}[/tex] = 2 [tex]t_{2}[/tex]
Also ,
total distance covered = 30 [tex]t_{1}[/tex] + 60 [tex]t_{2}[/tex]
Average speed = total distance / total time
= 30 [tex]t_{1}[/tex] + 60 [tex]t_{2}[/tex] / [tex]t_{1}[/tex] +[tex]t_{2}[/tex]
Recall that [tex]t_{1}[/tex] = 2 [tex]t_{2}[/tex] , substitute this into the formula for average speed , then we have
Average speed = 30(2[tex]t_{2}[/tex]) +60 [tex]t_{2}[/tex] / 3[tex]t_{2}[/tex]
Average speed = 120[tex]t_{2}[/tex] / 3[tex]t_{2}[/tex]
Therefore :
Average speed = 40 mi/hr
