Question

Each week, Rosario drives to an ice-skating rink that is 60 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? StartFraction 60 Over 55 EndFraction StartFraction 60 Over x EndFraction = 2. 75 StartFraction 60 Over 55 EndFraction times StartFraction 60 Over x EndFraction = 2. 75 60 (55) 60 x = 2. 75 60 (55) times 60 x = 2. 75.

Answer 1

Rosario's average speed on her way home is 36.66 miles per hour.

Average speed

Given that each week, Rosario drives to an ice-skating rink that is 60 miles away, and the round-trip takes 2.75 hours, to determine, if she averages 55 miles per hour on his way to the rink, what is her average speed to return to his house, the following calculation must be made:

• 55 = 1
• 60 = X
• 60 / 55 = X
• 1.09 = X
• 2.75 - 1.09 = 1.66
• 55 = 1
• 27.5 = 2
• 55 / 3 x 2 = 36.66

Therefore, Rosario's average speed on her way home is 36.66 miles per hour.

Learn more about averages in brainly.com/question/12322912

Answer 2

The average speed is the rate at which the total distance is traveled in the time taken.

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

$\dfrac{60}{55} +\dfrac{60}{x} =2.75$

What is average speed?

The average speed is the rate at which the total distance is traveled in the time taken. Rate of speed can be given as,

$s=\dfrac{x}{t}$

Here, $x$ is the distance traveled by the object and $t$ is time taken but the object to cover that distance.

Given information-

Rosario drives to an ice-skating rink each week that is 60 miles away.

The total time round-trip takes is 2.75 hours.

The average speed of drive is 55 miles per hour.

The number of miles per hour he averages on his way home is $x$.

The average speed of drive is 55 miles per hour and the total distance is 60 miles. Let $t_1$ is the time taken to travel in the way of his wink. Thus using the above formula,

$55=\dfrac{60}{t_1} \\t_1=\dfrac{60}{55}$

As Rosario drives to 60 miles from ice-skating rink to home with average speed of $x$ miles per hour. Let $t_2$ is the time taken by him to come back to the home. Thus,

$t_2=\dfrac{60}{x}$

As the total time taken by him is 2.75 hours. Thus the sum of both the time obtained is equal to the 2.75. Hence,

$t_1+t_2=2.75$

Put the values,

$\dfrac{60}{55} +\dfrac{60}{x} =2.75$

This is the required equation. Solving further,

$\dfrac{60}{55} +\dfrac{60}{x} =2.75\\\dfrac{60x+3300}{55x} =2.75\\{60x+3300}=151.25x\\151.25x-60x=3300\\91.25x=3300\\x=36.164$

Hence the value of the $x$ is 36.164.

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

$\dfrac{60}{55} +\dfrac{60}{x} =2.75$

Learn more about the rate of speed here.

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