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3 years ago

8

Arlington and Vernonville are 160 miles apart. A car leaves Arlington traveling towards Vernonville, and another car leaves Ver

nonville at the same time, traveling towards Arlington. The car leaving Arlington averages 10 miles per hour more than the other, and they meet after 1 hour and 36 minutes. What are the average speeds of the cars?1. The car leaving Arlington averages_______MPH2. The car leaving Vernonville averages_______MPH

2 answers:

Volgvan3 years ago

8 0

Answer:

The car leaving Arlington averages 55 mph.

The car leaving Vernonville averages 45 mph.

Step-by-step explanation:

Hi there!

The traveled distance can be calculated as follows:

d = v · t

Where

d = traveled distance at time t.

v = speed.

t = time.

The cars meet after 1 h and 36 min, let´s convert it to hours only:

36 min · (1 h/60 min) = 0.6 h

Then, the cars meet at t = 1.6 h

We have the following equations:

d₁ + d₂ = 160 miles

d₁ = v₁ · 1.6 h

d₂ = v₂ · 1.6 h (v₂ = v₁ - 10 mph)

d₂ = (v₁ - 10 mph) · 1.6 h

Where:

d₁ = distance traveled by the car leaving Arlington

d₂ = distance traveled by the car leaving Vernonville.

v₁ = speed of the car leaving Arlington.

v₂ = speed of the car leaving Vernonville.

Then, let´s solve this system of equations:

d₁ + d₂ = 160 miles

v₁ · 1.6 h + (v₁ - 10 mph) · 1.6 h = 160 mi

divide both sides of the equation by 1.6 h:

v₁ + v₁ - 10 mph = 100 mph

add 10 mph to both sides of the equation:

2v₁ = 110 mph

divide by 2 the both sides of the equation:

v₁ = 55 mph

v₂ = v₁ - 10 mph = 55 mph - 10 mph = 45 mph

The car leaving Arlington averages 55 mph.

The car leaving Vernonville averages 45 mph.

Have a nice day!

makkiz [27]3 years ago

7 0

Answer:Arlington moves at 55miles/hr

Vernon ville moves at 45 miles/hr

Step-by-step explanation:

Let a be the speed of the car leaving Arlington

Let v be the speed of the car leaving

Vernon ville

a = v+10

Distance travelled by the car leaving Arlington after 1hr 36minutes(1.6hrs)

= speed × time = 1.6a

Distance travelled by the car leaving Vernon ville after 1hr 36minutes(1.6hrs)

= speed × time = 1.6v

They meet after travelling this distance each thus covering 160 miles

1.6a + 1.6v = 160 --------1

a = v +10 (a is faster with 10miles/hr)

Put a in eqn 1

1.6(v+10) + 1.6v = 160

1.6v + 16 + 1.6v = 160

3.2v = 160-16=144

v =45 miles/hr

a =45+10= 55miles/hr

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