Respuesta :
Answer:
The speed of the motorcycle is 62 miles per hour and of the car is 72 miles per hour.
Step-by-step explanation:
The equation for the velocity is given by:
[tex]v = \frac{d}{t}[/tex]
In which d is the distance and t is the time.
Motorcycle:
Velocity v, d = 248. Then
[tex]v = \frac{248}{t}[/tex]
Car:
Velocity v+10, d = 288. Then
[tex]v + 10 = \frac{288}{t}[/tex]
From the first equation:
[tex]v = \frac{248}{t}[/tex]
[tex]vt = 248[/tex]
[tex]t = \frac{248}{v}[/tex]
Replacing in the second:
[tex]v + 10 = \frac{288}{t}[/tex]
[tex]v + 10 = \frac{288}{\frac{248}{v}}[/tex]
[tex]v + 10 = \frac{288v}{248}[/tex]
[tex]288v = 248(v + 10)[/tex]
[tex]288v = 248v + 2480[/tex]
[tex]40v = 2480[/tex]
[tex]v = \frac{2480}{40}[/tex]
[tex]v = 62[/tex]
The speed of the motorcycle is 62 miles per hour and of the car is 72 miles per hour.
