Answer:
The speeds are 34 mph for the slower car and 68 mph for the faster car.
Step-by-step explanation:
speed = distance/time
Using s for speed, d for distance, and t for time, we have the equation for speed:
s = d/t
Solve for distance, d, by multiplying both sides by t.
d = st
Now we use the given information.
Speed of slower car: s
Speed of faster car: 2s
Distance traveled by faster car: d
Distance traveled by slower car: d - 204
time traveled by faster car = time traveled by slower car = 6
Distance equation for faster car:
d = st
d = 2s * 6
d = 12s <---- equation 1
Distance equation for slower car:
d = st
d - 204 = s * 6
d - 204 = 6s
d = 6s + 204 <----- equation 2
Now, using equations 1 and 2, we have a system of two equations in two unknowns.
d = 12s
d = 6s + 204
Since the first equation is already solved for d, we can use the substitution method. Substitute 12s for d in the second equation:
12s = 6s + 204
6s = 204
s = 34
The speed of the slower car is 34 mph.
The speed of the faster car is
2s = 2(34) = 68
The speed of the faster care is 68 mph.
