Two cars start out together from the same place. they travel in opposite directions, with one of them traveling 5 miles per hour faster than the other. after two hours, they are 262 miles apart. how fast is each car traveling?
Annotation General formula for distance-time-velocity relationship is as following d = v × t The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁. The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.
One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car. v₁ = v₂ + 5 (first equation)
The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below. d₁ + d₂ = 262 (second equation)
Plug the d-v-t relationship to the second equation d₁ + d₂ = 262 v₁ × t + v₂ × t = 262 v₁ × 2 + v₂ × 2 = 262 2v₁ + 2v₂ = 262
Plug the v₁ as (v₂+5) from the first equation 2v₁ + 2v₂ = 262 2(v₂ + 5) + 2v₂ = 262 2v₂ + 10 + 2v₂ = 262 4v₂ + 10 = 262 4v₂ = 252 v₂ = 252/4 v₂ = 63 The second car is 63 mph fast.
Find the velocity of the first car, use the first equation v₁ = v₂ + 5 v₁ = 63 + 5 v₁ = 68 The first car is 68 mph fast.
