Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 10 hours. When Maria drove home, there was no traffic and the trip only took 7 hours. If her average rate was 18 miles per hour faster on the trip home, how far away does Maria live from the mountains?

Question

anonymous · Answer

let Maria live x miles from the mountains 
 Let her rate to mountains be y 
 t=d/r 
 x/y = 9
 x=9y 
 Return trip 4 hours
 rate = y+40 
 x/(y+40) =4 
substitute x
 9y/(y+40)=4 
 9y=4y+160 
 9y-4y=160
 5y=160
 y= 160/5
 y=32 
 x=9y
 x=9*32= 288 miles 
 distance to the mountain = 288 miles