SOLUTION: A cyclyist bikes at a constant speed for 20 miles. He then returns home at the same speed but takes a different route. His return trip takesone hour longer and is 25 miles. Find h

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: A cyclyist bikes at a constant speed for 20 miles. He then returns home at the same speed but takes a different route. His return trip takesone hour longer and is 25 miles. Find h      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 79164: A cyclyist bikes at a constant speed for 20 miles. He then returns home at the same speed but takes a different route. His return trip takesone hour longer and is 25 miles. Find his speed.
Answer by checkley75(3666) About Me  (Show Source):
You can put this solution on YOUR website!
DISTANCE=RATE*TIME
25=R(T+1)
20=R*T OR R=20/T. NOW SUBSTITUTE 20/T FOR R IN THE FIRST EQUATION & SOLVE FOR TIME
25=20/T(T+1)
25=(20T+20)/T NOW CROSS MULTIPLY WE GET
25T=20T+20
25T-20T=20
5T=20
T=4 IS THE TIME FOR THE FIRST TRIP.
THUS 20/4=5 MPH IS THE SPEED.
25/(4+1)=25/5=5 MPH.