Answer:
Chang live 480 miles from the mountains
Explanation:
Constant Speed Motion
An object is said to have constant speed if it takes the same time t to travel the same distances x. The speed is calculated as
[tex]\displaystyle v=\frac{x}{t}[/tex]
From that equation, we can solve for x
[tex]x=v\cdot t[/tex]
and for t
[tex]\displaystyle t=\frac{x}{v}[/tex]
Let's assume the distance from the mountains and Chang's house is x. We know he took t1=12 hours in heavy traffic at an average speed v1, thus we can set
[tex]x=v_1\cdot t_1[/tex]
In his way back home Chang took t2=8 hours at a speed v2, thus:
[tex]x=v_2\cdot t_2[/tex]
Since the distance is the same
[tex]v_1\cdot t_1=v_2\cdot t_2[/tex]
The speed back is 20 mph more than the speed to the mountain:
[tex]v_2=v_1+20[/tex]
Replacing in the above equation
[tex]v_1\cdot t_1=(v_1+20)\cdot t_2[/tex]
[tex]v_1\cdot t_1=v_1\cdot t_2+20\cdot t_2[/tex]
[tex]v_1\cdot 12=v_1\cdot 8+20\cdot 8[/tex]
Solving for v1
[tex]v_1\cdot 4=160[/tex]
[tex]v_1=40\ mph[/tex]
Now we can compute the value of x
[tex]x=40\cdot 12[/tex]
[tex]\boxed{x=480 \ miles}[/tex]
Chang lives 480 miles from the mountains
