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?

Question

10-02-2018
Mathematics

contestada

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?

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gustanika gustanika · Answer 1 · 2018-02-10T09:53:44+01:00

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.

Answer
[tex]\boxed{\boxed{ v_{1}=68mph} }[/tex]
[tex]\boxed{\boxed{ v_{2}=63mph} }[/tex]

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?

Respuesta :

Otras preguntas

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?