SOLUTION: A cyclist bikes at a constant speed for 25 miles. He then returns home at the same speed but takes a different route. His return trip takes 1 hour longer and is 30 miles. Find h

Question 1007801: A cyclist bikes at a constant speed for 25 miles. He then returns home at the same speed but takes a different route. His return trip takes 1 hour longer and is 30 miles. Find his speed?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
where is distance, is speed, and is time
if a cyclist bikes at a constant speed for , we have
..............solve for
.......eq.1
if he then returns home at the same speed but takes a different route, and his return trip takes longer and is , we have
.............solve for
.........eq.2
eq.1 and eq.2 have equal left sides, so make equal right sides and solve for
.......cross multiply

hours
now find
.......eq.1

=> speed
and
.........eq.2

=> speed on his return trip
so, in both directions his speed was constant and it was

Answer by MathTherapy(10549) (Show Source): You can put this solution on YOUR website!
A cyclist bikes at a constant speed for 25 miles. He then returns home at the same speed but takes a different route. His return trip takes 1 hour longer and is 30 miles. Find his speed?

Let speed be S
Then time on outbound trip =
Time taken on return trip =
Time equation formed:
25 = 30 � S ------- Multiplying by LCD, S
S, or speed = 30 � 25, or mph
RELATED QUESTIONS
A cyclist bikes at a constant speed for 25 miles. He then returns home at the same speed... (answered by jorel1380)
A cyclist bikes at a constant speed for 20 miles. He then returns home at the same speed... (answered by KMST)
A cyclist bikes at a constant speed for 23 miles. He then returns home at the same speed... (answered by ewatrrr)
A cyclist bikes at a constant speed for 18 miles. He then returns home at the same speed... (answered by htmentor)
A cyclyist bikes at a constant speed for 20 miles. He then returns home at the same... (answered by checkley75)
Cyclist bikes at a constant speed for 22 miles. He returns home at that speed but takes... (answered by josgarithmetic)
A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed... (answered by ankor@dixie-net.com)
a cyclist bikes at a constant speed for 19 miles.He then returns home at the same speed... (answered by josmiceli)
A cyclist bikes at a constant speed for 24 miles. He then returns home at the same speed (answered by Paul)