Question

Trey drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 12 hours. When Trey drove home, there was no traffic and the trip only took hours. If his average rate was 20miles per hour faster on the trip home, how far away does Trey live from the mountains?
Do not do any rounding.

Answer 1

Question was Incomplete;Complete question is given below;

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

Do not do any rounding.

Answer:

Trey lives 480 miles from the mountain.

Step-by-step explanation:

Given:

Time taken to drove the mountain =12 hours

Time taken to return back from mountain = 8 hours.

Let the speed at which he drove to mountain be denoted by 's'.

Speed on the trip to home = $s+20$

We need to find the distance Trey live from the mountains.

Solution:

Let the distance be denoted by 'd'.

Now we know that;

Distance is equal to speed times Time.

framing in equation form we get;

distance from home to mountain $d=12s$

Also distance from mountain to home $d = (s+20)8=8s+160$

Now distance is same for both the trips;

so we can say that;

$12s=8s+160$

Combining the like terms we get;

$12s-8s=160\\\\4s=160$

Dividing both side by 4 we get;

$\frac{4s}{4}=\frac{160}{4}\\\\s=40\ mph$

Speed while trip to mountain = 40 mph

Speed while trip to home = $s+20=420+20=60\ mph$

So Distance $d=12s=12\times40 = 480\ miles$

Hence Trey lives 480 miles from the mountain.