Maria drove to the mountains last weekend. There was heavy traffic on the way there, and the trip took 9 hours. When Maria 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 Maria live from the mountains?

• Time taken for trip from home to mountains=9h
  Time taken for trip from mountains to home=4h
  Let distance from home to mountains=x miles
  let avg speed from home to mountains=y miles/h
  Given avg speed on the trip home is 40m/h faster than speed from home to mountains=y+40 m/h
  => (x/9)=y and (x/4)=y+40
  by solving this, we get y=32 m/h and the distance x=32*9=288 miles...
• 11 years agoHelpfull: Yes(34) No(2)
• let the dist be D.
  avg speed = (2*xy)/x+y
  x,y are the different speeds.
  so 40={2*(D/9)*(D/4)}/(D/9+D/4)
  =>D=260 miles
• 11 years agoHelpfull: Yes(12) No(6)
• let speed is x milesph from home to mountain due to traffic
  so distance from home to mountain=x*9
  now distance from mountain to home=(x+40)*4
  since distance is same form home to mountain and mountain to home
  9x=(x+40)4
  5x=160
  x=32
  so distance is 9x=9*32=288 miles
• 11 years agoHelpfull: Yes(12) No(0)
• time taken from home to mountains = 9 hrs
  time taken from mountains to home = 4 hours.
  total time taken = 13 hrs
  but average speed = 40 mile per hrs
  so distance covered = avg speed*total time taken
  = 40 * 13
  = 520
  so distance from mountain to home = 520/2 = 260 (ans)
• 11 years agoHelpfull: Yes(10) No(9)
• (s1+s2)/2=((d/t1)+(d/t2))/2
  40=((d/t1)+(d/t2))/2
  40=((d/9)+(d/4))/2
  80=((d/9)+(d/4))
  d=2880/13
• 11 years agoHelpfull: Yes(4) No(7)
• x be the distance from mountains
  s1 (speed while going mountains)= x/9
  s2 (speed while coming back from mountains)= x/4
  Acc. to ques, x/9 + 40 = x/4
  40= 0.13889x
  x= 287.9977 miles away from mountains
• 11 years agoHelpfull: Yes(4) No(1)
• 2880/13=221.538 miles
  
• 11 years agoHelpfull: Yes(1) No(9)
• 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
  
• 11 years agoHelpfull: Yes(1) No(0)
• let speed =x and distance=speed*time
  so while driving toward mountain distance=x*9
  and while returning distance=4(x+40)
  by equating both
  9x=4x+160
  =>x=32
  distance=288
  
• 11 years agoHelpfull: Yes(1) No(0)
• d/4-d/9=40
  5d/36=40
  d=280ans
• 11 years agoHelpfull: Yes(0) No(2)
• totsl distance is 40*4=160 miles
  time taken ( hours that means speed=160/9=17.7miles
• 11 years agoHelpfull: Yes(0) No(1)
• 72 miles thanks
• 9 years agoHelpfull: Yes(0) No(1)