Taking into account the definition of speed, you get that the average speed of the entire trip is 53.33 [tex]\frac{mi}{hr}[/tex] .
It is necessary to know that speed is a quantity that expresses the relationship between the space traveled by an object and the time used for it.
In other words, speed can be defined as the amount of space traveled per unit of time with which a body moves and can be calculated using the expression:
[tex]speed= \frac{distance traveled}{time}[/tex]
In this case, you know that the shipping mall is 40 miles from the woman's house and that she is going to the mall and back home. So it runs the 40 miles of distance twice. So the distance traveled is 80 miles.
On the other hand, you know that on the trip to the mall she averages 80 [tex]\frac{mi}{hr}[/tex]. Since the woman travels the first 40 miles at that speed, and taking into account the definition of speed, the time it takes to go to the shopping mall is calculated as:
[tex]80\frac{mi}{hr} = \frac{40 mi}{time}[/tex]
Solving:
time× 80 [tex]\frac{mi}{hr}[/tex]= 40 mi
[tex]time = \frac{40 mi}{80\frac{mi}{hr}}[/tex]
time=0.5 hr
Finally, you know that on the return trip she averages just 40 [tex]\frac{mi}{hr}[/tex]. Since the woman travels the second 40 miles at that speed, and taking into account the definition of speed, the time it takes to return to her home is calculated as:
[tex]40\frac{mi}{hr} = \frac{40 mi}{time}[/tex]
Solving:
time× 40 [tex]\frac{mi}{hr}[/tex]= 40 mi
[tex]time = \frac{40 mi}{40\frac{mi}{hr}}[/tex]
time=1 hr
Then, the total time of the trip, which consists of going to the shopping mall and returning home, is calculated as:
total time= 0.5 hr + 1 hr
total time= 1.5 hr
Finally, taking into account the definition of speed, average speed of the trip is calculated as:
[tex]speed= \frac{80 miles}{1.5 hr}[/tex]
Solving:
speed= 53.33 [tex]\frac{mi}{hr}[/tex]
In summary, the average speed of the entire trip is 53.33 [tex]\frac{mi}{hr}[/tex] .
Learn more about average speed:
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