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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, which equation can be used to find x, the number of miles per hour he averages on his way home?

Sagot :

Davidyangnycidn
120/(2.75-(120/55))= x the mph on the way home

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.

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