SOLUTION: Please help me solve this equation: I've scoured the website, but I can't find one specifically like this one. Distance, Rate and Time John and Mary leave their house at the sam

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Please help me solve this equation: I've scoured the website, but I can't find one specifically like this one. Distance, Rate and Time John and Mary leave their house at the sam      Log On


   

Question 743648: Please help me solve this equation: I've scoured the website, but I can't find one specifically like this one.
Distance, Rate and Time
John and Mary leave their house at the same time and drive in opposite directions. John drives at 60 mph and travels 35 mi farther than Mary, who drives at 40 mph. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?
Thanks!
Found 2 solutions by josmiceli, mananth:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = distance in miles that Mary travels
+d+%2B+35+ = distance in miles that John travels
Let +t+ = time in hours that John's trip takes
+t+%2B+1%2F4+ = time in hours that Mary's trip takes
------------------
John's equation:
(1) +d+%2B+35+=+60t+
Mary's equation:
(2) +d+=+40%2A%28+t+%2B+1%2F4+%29+
-----------------------
(2) +d+=+40t+%2B+10+
Substitute (2) into (1)
(1) +40t+%2B+10+%2B+35+=+60t+
(1) +20t+=+45+
(1) +t+=+2.25+
and
+t+%2B+1%2F4+=+2.5+
John drives for 2 hrs 15 min
Mary drives for 2 hrs 30 min
check:
(1) +d+%2B+35+=+60%2A2.25+
(1) +d+=+135+-+35+
(1) +d+=+100+
and
(2) +d+=+40%2A%28+2.25+%2B+1%2F4+%29+
(2) +d+=+40%2A2.5+
(2) +d+=+100+
OK

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
John and Mary leave their house at the same time and drive in opposite directions. John drives at 60 mph and travels 35 mi farther than Mary, who drives at 40 mph. Mary's trip takes 15 min longer than John's. For what length of time does each of them drive?
let Mary travel x miles
Mary speed = 40 mph
Mary's time = x/40
John will drive x+35 miles
John speed = 60 mph
john's time = (x+35)/60
Mary's time - John's time = 1/4 hour
x/40 - (x+35)/60 = 1/4
LCD = 120
multiply eqn by 120
3x-2(x+35)=30
3x-2x-70=30
x-70=30
x=100 miles=> distance driven by Mary
distance driven by John = 135
Time taken by Mary = 100/40 = 2.5 hours
Time taken by John =135/60 = 2.25 hours