Problema Solution
Two cars leave towns 720 kilometers apart at the same time and travel toward each other. One car's rate is 12 kilometers per hour more than the other's. If they meet in 4 hours, what is the rate of the faster car?
Answer provided by our tutors
let
t = 4 hr the time of the travel
d1 = the distance the first car travels
d2 = the distance the second car travels
v= the rate of the first car
v + 12 = the rate of the second car
d1 + d2 = 720 km
since speed = distance/time = > time = distance/speed
d1/v = t
d1/v = 4
d1 = 4v
d2/(v +12) = t
d2/(v +12) = 4
d2 = 4(v + 12)
plug d1 = 4v and d2 = 4(v + 12) into d1 + d2 = 720 km
4v + 4(v + 12) = 720
by solving we find
v = 84 km/h
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v + 12 = 84 +12 = 96 km/h
the rate of the faster car is 96 km/h.