Answer:
Motorcycle : 40 miles per hour
Car: 50 miles per hour
Step-by-step explanation:
Hi, we have to write a system of equations.
The average speed of the car is 30 mph slower than twice the speed of the motorcycle.
- C = 2 M -30 (first equation)
Where
C = speed rate of the car
M = speed rate of the motorcycle
since distance = speed x time
In two hours(time), the car is 20 miles(distance) ahead of the motorcycle.
Since the car is ahead of the motorcycle , the speed is the difference of both.(C-M)
- 20 = (C-M) 2 (second equation)
Replacing the value of C by 2 M -30 , in the second equation:
20 = [(2M-30)-M ]2
20 = [M-30]2
20 = 2M-30(2)
20= 2M -60
20+60 =2M
80 = 2M
80/2 =M
M =40 km per hour
Replacing M in the first equation:
C = 2 (40)-30 = 80-30
C = 50 km per hour
