Question

Chang drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Chang drove home, there was no traffic and the trip only took 8 hours. If his average rate was 20 miles per hour faster on the trip home, how far away does Chang live from the mountains?

Answer 1

Chang live 480 miles from the mountains

Step-by-step 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

`\displaystyle v=(x)/(t)`

From that equation, we can solve for x

`x=v\cdot t`

and for t

`\displaystyle t=(x)/(v)`

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

`x=v_1\cdot t_1`

In his way back home Chang took t2=8 hours at a speed v2, thus:

`x=v_2\cdot t_2`

Since the distance is the same

`v_1\cdot t_1=v_2\cdot t_2`

The speed back is 20 mph more than the speed to the mountain:

`v_2=v_1+20`

Replacing in the above equation

`v_1\cdot t_1=(v_1+20)\cdot t_2`

`v_1\cdot t_1=v_1\cdot t_2+20\cdot t_2`

`v_1\cdot 12=v_1\cdot 8+20\cdot 8`

Solving for v1

`v_1\cdot 4=160`

`v_1=40\ mph`

Now we can compute the value of x

`x=40\cdot 12`

`\boxed{x=480 \ miles}`

Chang lives 480 miles from the mountains