A cyclyist bikes at a constant speed for 20 miles He then re

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.

Solution

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.