SOLUTION: If I travel for one hour from my house to my friend's house at a rate of 9mph on flat ground, 6mph when the terrain is uphill and 18mph when the terrain is downhill, how many miles

Algebra ->  Length-and-distance -> SOLUTION: If I travel for one hour from my house to my friend's house at a rate of 9mph on flat ground, 6mph when the terrain is uphill and 18mph when the terrain is downhill, how many miles      Log On


   

Question 186895: If I travel for one hour from my house to my friend's house at a rate of 9mph on flat ground, 6mph when the terrain is uphill and 18mph when the terrain is downhill, how many miles is it from my house to my friend's house?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It's not real clear, but I assume the whole trip
takes 1 hr.
Let t%5B1%5D = time for the portion on flat ground
Let d%5B1%5D = distance for the portion on flat ground
Let t%5B2%5D = time for uphill portion
Let d%5B2%5D = distance for the uphill portion
Let t%5B3%5D = time for downhill portion
Let d%5B3%5D = distance for the downhill portion
given:
(1) t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+1 hr
(2) d%5B1%5D+=+9%2At%5B1%5D
(3) d%5B2%5D+=+6%2At%5B2%5D
(4) d%5B3%5D+=+18%2At%5B3%5D
--------------------
What I need to find is d+=+d%5B1%5D+%2B+d%5B2%5D+%2B+d%5B3%5D
Rewrite (2),(3) and (4) like this:
(2) t%5B1%5D+=+d%5B1%5D%2F9
(3) t%5B2%5D+=+d%5B2%5D%2F6
(4) t%5B3%5D+=+d%5B3%5D%2F18
Add the 3 equations
d%5B1%5D%2F9+%2B+d%5B2%5D%2F6+%2B+d%5B3%5D%2F18+=+t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D
d%5B1%5D%2F9+%2B+d%5B2%5D%2F6+%2B+d%5B3%5D%2F18+=+1
Write the left side with 18 as denominators
2%2Ad%5B1%5D%2F18+%2B+3%2Ad%5B2%5D%2F18+%2B+d%5B3%5D%2F18+=+1
If d%5B1%5D+=+3,
and d%5B2%5D+=+2,
d%5B3%5D+=+6
The left side is 18%2F18+=+1
d+=+d%5B1%5D+%2B+d%5B2%5D+%2B+d%5B3%5D+=+3+%2B+2+%2B+6
3+%2B+2+%2B+6+=+11 mi
It is 11 miles between houses
check answer:
(2) t%5B1%5D+=+d%5B1%5D%2F9
(2) t%5B1%5D+=+1%2F3
(3) t%5B2%5D+=+d%5B2%5D%2F6
(3) t%5B2%5D+=+1%2F3
(4) t%5B3%5D+=+d%5B3%5D%2F18
(4) t%5B3%5D+=+1%2F3
(1) t%5B1%5D+%2B+t%5B2%5D+%2B+t%5B3%5D+=+1 hr
(1) 1%2F3+%2B+1%2F3+%2B+1%2F3+=+1 hr