Amy drove to the mountains last weekend. there was heavy traffic on the way there, and the trip took 8 hours. when amy drove home, there was no traffic and the trip only took 5 hours. if her average rate was 21 miles per hour faster on the trip home, how far away does amy live from the mountains?
do not do any rounding.

280 miles

Step-by-step explanation:

From Amy's house to the mountains with traffic

Distance = x

time = 8 hrs

speed = Y

From the mountains back home, No traffic

Distance = x

time 5hrs

Speed = Y +21

now we know that the distance is the same (i.e. distance from her house to and fro the mountain won't change)

distance = speed x time

so our formular is

distance x = 8Y with traffic equation 1

distance x = 5(y+21) without traffic-- equation 2

substitute eqn 1 into 2 it becomes

8Y = 5Y + 105

8Y-5Y = 105

3Y = 105

Y = 35miles per hour.

so. distance x = 8 x 35 = 280miles away.

Amy lives 280 miles away