SOLUTION: Mitchel drove to a friend at a rate of 40 miles/hr. He returned by the same route at a rate of 45 miles/hr.The driving time for the round trip was 4 hours.What is the distance Mitc

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: Mitchel drove to a friend at a rate of 40 miles/hr. He returned by the same route at a rate of 45 miles/hr.The driving time for the round trip was 4 hours.What is the distance Mitc      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 152596: Mitchel drove to a friend at a rate of 40 miles/hr. He returned by the same route at a rate of 45 miles/hr.The driving time for the round trip was 4 hours.What is the distance Mitchel travelled ?
Answer by Earlsdon(6103) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the distance formula: d+=+r%2At where: d = distance, r = rate (speed), and t = time of travel.
For the outbound trip:
d%5B1%5D+=+r%5B1%5D%2At%5B1%5D
For the return trip:
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D
In this problem, d%5B1%5D+=+d%5B2%5D and t%5B1%5D%2Bt%5B2%5D+=+4, so you can write:
r%5B1%5D%2At%5B1%5D+=+r%5B2%5D%2At%5B2%5D
r%5B1%5D+=+40 and r%5B2%5D+=+45 These are given, so...
40%2At%5B1%5D+=+45%2At%5B2%5D Substitute: t%5B2%5D+=+4-t%7B1%5D
40%2At%5B1%5D+=+45%2A%284-t%5B1%5D%29 Simplify and solvefor t%5B1%5D
40%2At%5B1%5D+=+180-45%2At%5B1%5D Add 45%2At%5B1%5D to both sides.
85%2At%5B1%5D+=+180 Divide both sides by 85.
t%5B1%5D+=+2.12hours.
Now you can calculate the one-way distance, d%5B1%5D
d%5B1%5D+=+40%2At%5B1%5D
d%5B1%5D+=+40%2A2.12
d%5B1%5D+=+84.8miles.
This should be equal to d%5B2%5D...let's see if it is:
d%5B2%5D+=+r%5B2%5D%2At%5B2%5D Substitute r%5B2%5D+=+45 and t%5B2%5D+=+4-2.12=1.88
d%5B2%5D+=+45%2A1.88
d%5B2%5D+=+84.6miles.
Michael travelled d%5B1%5D%2Bd%5B2%5D+=+84.8%2B84.6=169.4miles.