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

Question:

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

Do not do any rounding.

480 miles

That is Teresa lives 480 miles  from the mountains

Explanation:

Here we have

Distance D = Speed S × Time t

On her way to the mountain we have

D = S × 12

On her way back we have

D = (S +20)×8

Therefore, by comparing the two above equations, we have

S × 12 = (S +20)×8

Therefore, 12·S = 8·S +160 or

4·S = 160

Hence S = 160/4 = 40 miles/hour

Therefore, from D = S × 12, we have

D = 40 × 12 = 480 miles.

The complete question is ;

Teresa drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took

12 hours. When Teresa drove home, there was no traffic and the trip only took 8 hours. If her average rate was 20 miles per hour faster on the trip home, how far away does Teresa live from the mountains?

Do not do any rounding.

Teresa lives 480 miles from the mountains

Explanation:

We know that distance = rate x time

Thus, we will call rate v, and call time t and call distance d.

Now, when teresa was going to the mountain, we are told that the trip took 12 hours.

Thus, distance covered is; d = v x 12

d = 12v - - - - - (eq1)

Now, when Teresa was going home we are told the trip took 8 hours and the rate of change was 20 miles per hour faster. This means that rate of change is v + 20 since the rate of change on the trip to the mountain was v.

Thus,

d = (v + 20) x 8 - - - - (2)

Equating eq(1) to eq(2), we have;

12v = 8(v + 20)

Expanding, we have,

12v = 8v + 160

Subtract 8v from both sides to get ;

4v = 160

Divide both sides by 4;

v = 160/4 = 40 miles per hour

Let's put this value for v in eq(1);

d = 12v = 12(40)

d = 480 miles