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A car is traveling on a small Highway and it is either going 55 miles per hour or 35 miles per hour depending on the speed limit until it reaches its destination 200 miles away letting X represent the amount of time and hours that the car is going 55 miles per hour and wiping the time and hours of the car is going 35 miles per hour equation describing the relationship is 55x + 35 y equals 200 with the car speeds 2.5 hours going 35 miles per hour on the ship how long does it spend going 55 miles per hour

Respuesta :

Answer:

The car spends approximately 2.045 hours going 55 miles per hour.

Step-by-step explanation:

This problem is described by the formula:

[tex] \\ 55x + 35y = 200[/tex] [1]

We need to remember that:

[tex] \\ Speed = \frac{distance}{time}[/tex]

We can solve this equation for distance multiplying each member of the equation by time:

[tex] \\ Speed\;*\;time = \frac{distance}{time}*\;time[/tex]

[tex] \\ Speed\;*\;time = distance\;*\frac{time}{time}[/tex]

[tex] \\ Speed\;*\;time = distance\;*1[/tex]

[tex] \\ distance = Speed\;*\;time[/tex]

(Remember that any element divided by itself is 1.)

So, the result of equation [1] is distance.

But the distance is different depending upon the time x the car spends traveling at a speed of 55 miles per hour or time y traveling at 35 miles per hour.

We also know that the total distance is 200 miles (also given in equation [1]).

Then, "if the car spends 2.5 hours going 35 miles per hour", how long does it spend going 55 miles per hour?

We need here to solve the equation for time x because it corresponds to the speed of 55 miles per hour to finally solve the question. We also need to substitute the value of y = 2.5 hours in the equation.

So

[tex] \\ 55x + 35y = 200[/tex]

[tex] \\ 55x + 35\frac{miles}{hour}*2.5\;hour = 200\;miles[/tex]

[tex] \\ 55x + 35*2.5\;miles*\frac{hour}{hour} = 200\;miles[/tex]

[tex] \\ 55x + 35*2.5\;miles*1 = 200\;miles[/tex]

[tex] \\ 55x + 87.5\;miles = 200\;miles[/tex]

Subtracting 87.5 from both sides of the equation:

[tex] \\ 55x + 87.5\;miles - 87.5\;miles = 200\;miles-87.5\;miles[/tex]

[tex] \\ 55x + 0 = 112.5\;miles[/tex]

[tex] \\ 55x = 112.5\;miles[/tex]

Dividing both sides of the equation by [tex]55\frac{miles}{hour}[/tex]:

[tex] \\ \frac{55*x}{55} = \frac{112.5\;miles}{55\frac{miles}{hour}}[/tex]

[tex] \\ \frac{55}{55}*x = \frac{112.5\;miles}{55\frac{miles}{hour}}[/tex]

[tex] \\ 1*x = \frac{112.5\;miles}{55\frac{miles}{hour}}[/tex]

[tex] \\ x = \frac{112.5}{55}\frac{miles}{\frac{miles}{hour}}[/tex]

[tex] \\ x = \frac{112.5}{55}\;miles*\frac{hour}{miles}[/tex]

[tex] \\ x = \frac{112.5}{55}\;hour*\frac{miles}{miles}[/tex]

[tex] \\ x = \frac{112.5}{55}\;hour*1[/tex]

[tex] \\ x = \frac{112.5}{55}\;hour[/tex]

[tex] \\ x =2.045\;hour[/tex]

Then, it spends approximately 2.045 hours going 55 miles per hour.

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