A car and a motorcycle leave at noon from the same location, heading in the same direction. The average speed of the car is 30 mph slower than twice the speed of the motorcycle. In two hours, the car is 20 miles ahead of the motorcycle. Find the speed of both the car and the motorcycle, in miles per hour.

Question

xxbatmanevoxx · Answer

@mazmaz1 I need help

czesc · Answer

Here's what we know:
D = r * t (Distance = rate * time)
c = 2m - 30 mph (car's rate is twice motorcycle minus 30)
D = 2m (motorcycle's rate after 2 hours is Distance)
D + 20 = (2m - 30 mph)2
(the car's Distance is 20 miles further at its own rate)
 
We have a value for D, so we can put that into the equation:
2m + 20 = (2m - 30 mph)2
2m + 20 = 4m - 60
-2m = -80
m = 40
 
Now that we know the motorcycle's rate, we can find the car's
c = 2*4 -30
c = 80 - 30
c = 50
 
now to check:
40 * 2 = 80
50 * 2 = 100
100 - 80 = 20
So the motor cycles was going 40 mph and the car 50 mph.

agent0smith · Answer

@czesc why not just link your source: https://www.wyzant.com/resources/answers/115133/word_problem

anonymous · Answer

let speed of car=x
speed of motor cycle=y
x=2y-30
after two hours
2x-2y=20
x-y=10
(2y-30)-y=10
y-30=10
y=40mph
x=2*40-30=50 mph