Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took hours. When Lucy 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 Lucy live from the mountains?

The question is incomplete, the complete complete question will be:

Lucy drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Lucy drove home, there was no traffic and the trip only took 4 hours. If her average rate was 40 miles per hour faster on the trip home, how far away does Lucy live from the mountains?

Lucy live at a distance of 288 miles from the mountains.

Step-by-step explanation:

DATA:

To the mts DATA:

Time = 9 hrs

Rate = r mph

Distance = 9r miles

From the mts DATA:

time = 4 hrs  

rate = r+40 mph  

distance = 4(r+40) miles

SOLUTION

Distance to = Distance from

9r = 4r + 160

5r = 160

r = 32 mph

RESULT:

Distance = 9r = 9*32 = 288 miles

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.