Answer:
The required equation is [tex]2.75=\frac{120}{55}+\frac{120}{x}[/tex]
The value of x is 211.2 miles per hour.
Step-by-step explanation:
Given : Each week, Rosario drives to an ice skating rink that is 120 miles away. The round-trip takes 2.75 hours. If he averages 55 miles per hour on his way to the rink.
To find : Equation can be used to find x, the number of miles per hour he averages on his way home?
Solution :
Firstly the distance is 120 miles.
If the average speed is 55 miles per hour.
The time taken is calculated by the formula
[tex]\text{Time}=\frac{\text{Distance}}{\text{Speed}}[/tex]
[tex]T_1=\frac{120}{55}[/tex]
If the average speed is x miles per hour.
[tex]T_2=\frac{120}{x}[/tex]
We have given that Total time taken for a trip is 2.75 hours
So, we add both the time
[tex]T=T_1+T_2[/tex]
[tex]2.75=\frac{120}{55}+\frac{120}{x}[/tex]
The required equation is [tex]2.75=\frac{120}{55}+\frac{120}{x}[/tex]
Now, we find the value of x,
Taking LCM in required equation,
[tex]2.75=\frac{120x+120(55)}{55x}[/tex]
[tex]2.75\times55x=120x+6600[/tex]
[tex]151.25x-120x=6600[/tex]
[tex]31.25x=6600[/tex]
[tex]x=\frac{6600}{31.25}[/tex]
[tex]x=211.2[/tex]
Therefore, The value of x is 211.2 miles per hour.