SOLUTION: a motor boat travelling at 18 miles per hour travellled the length of a lake in one quarterof an hour less time than it took when travelling at 12 miles per hour. what was the leng

Algebra ->  Conversion and Units of Measurement -> SOLUTION: a motor boat travelling at 18 miles per hour travellled the length of a lake in one quarterof an hour less time than it took when travelling at 12 miles per hour. what was the leng      Log On


   

Question 468959: a motor boat travelling at 18 miles per hour travellled the length of a lake in one quarterof an hour less time than it took when travelling at 12 miles per hour. what was the length in miles of the lake?
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Let d=distance, r=speed, t =time
d = r*t
******************
Trip 1:
t represents time to travel lake at 12 mph
d+=+18%28t-%281%2F4%29%29
Goal is to solve for d, so get t in terms of d
d%2F18+=+t+-+%281%2F4%29
%28d%2F18%29%2B%281%2F4%29+=+t
********************
Trip 2:
d+=+12t
d%2F12+=+t
*********************
Set equations equal to each other, since both are equal to t
d%2F12+=+%28d%2F18%29%2B%281%2F4%29
Eliminate fractions by multiplying equation by 36
LCM of 4,12,18 is 36 --> 4*9=36, 12*3 = 36, 18*2 =36
3d+=+2d+%2B+9
Subtract 2d on both sides
d+=+9
Length of lake is 9 mi.