Respuesta :
Answer:
The speed of the motorcycle is 66 miles per hour.
Step-by-step explanation:
We use the following relation to build a system of equations.
[tex]v = \frac{d}{t}[/tex]
In which v is the velocity, d is the distance, and t is the time.
Car:
[tex]v_{c} = \frac{d_{c}}{t}[/tex]
We have that the car travels 90 miles, so [tex]d_c = 90[/tex]
Then
[tex]v_{c} = \frac{90}{t}[/tex]
[tex]t = \frac{90}{v_{c}}[/tex]
a motorcycle travels 6 mph faster than a sport car.
This means that [tex]v_m = 6 + v_{c}[/tex], so [tex]v_{c} = v_m - 6[/tex]
Travels 99 miles, so [tex]d_m = 99[/tex]
[tex]v_{m} = \frac{99}{t}[/tex]
Since [tex]t = \frac{90}{v_{c}}[/tex] and [tex]v_{c} = v_m - 6[/tex], we have that [tex]t = \frac{90}{v_{m} - 6}[/tex]
So
[tex]v_{c} = \frac{99}{t}[/tex]
[tex]v_{m} = \frac{99}{\frac{90}{v_{m} - 6}}[/tex]
[tex]v_m = \frac{99(v_{m} - 6)}{90}[/tex]
[tex]99(v_{m} - 6) = 90v_m[/tex]
[tex]99v_m - 594 = 90v_m[/tex]
[tex]9v_m = 594[/tex]
[tex]v_m = \frac{594}{9}[/tex]
[tex]v_m = 66[/tex]
The speed of the motorcycle is 66 miles per hour.
