SOLUTION: Mike drove from New City to Old Village at an average speed of 60 m/h to visit his parents. On the way back he needed to speed up to catch a baseball game with a friend, so he drov

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Mike drove from New City to Old Village at an average speed of 60 m/h to visit his parents. On the way back he needed to speed up to catch a baseball game with a friend, so he drov      Log On

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Question 421237: Mike drove from New City to Old Village at an average speed of 60 m/h to visit his parents. On the way back he needed to speed up to catch a baseball game with a friend, so he drove at 75 m/h. His trip involved a total of 5 hours of driving time. What is the distance between New City and Old Village. (Any help would be much appreciated, i am doing questions for a practice exam.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
You need 2 equations, one for NYC to OV, and one for OV to NYC
Let d = distance from NYC to OV
Let t = time to go NYC to OV
------------------
NYC to OV
d+=+60%2At
OV to NYC
d+=+75%2A%285+-+t%29
--------------
This is 2 equations and 2 unknowns, so it's solvable
By substitution:
60t+=+75%2A%285+-+t%29
60t+=+375+-+75t
+135t+=+375
t+=+2.778
and
d+=+60t
d+=+60%2A2.778
d+=+166.67 mi
The distance is 166.67 miles
check answer:
d+=+75%2A%285+-+t%29
166.67+=+75%2A%285+-+2.778%29
166.67+=+75%2A2.222
166.67+=+166.65
close enough