Answer: the speeds of the cars are 47mph for the faster one, and 35mph for the slower one.
Step-by-step explanation:
Here you must remember the relation:
Speed = distance/time.
So we have car A and car B, with Sa the speed of car A, and Sb the speed of car B.
We know that:
Sa = Sb + 12mph.
and in the same time T, car A travels 141mi, while car B travels 105mi, then we have:
Sa*T = 141mi
Sb*t = 105mi
we can take the quotient of those two and get:
(Sa/Sb) = 141/105.
now we can replace Sa by Sa = Sb + 12mph.
(Sb + 12mph)/(Sb) = 141/105.
Sb + 12mph = (141/105)*Sb
Sb*(141/105 - 1) = 12mph
Sb = 12mph/(141/105 - 1) = 35mph.
and we know that:
Sa = Sb + 12mph = 35mph + 12mph = 47mph.