SOLUTION: A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find hi

Question 190828: A cyclist bikes at a constant speed for 17 miles. He then returns home at the same speed but takes a different route. His return trip takes one hour longer and is 22 miles. Find his speed.
I was trying to do this problem this way:
Distance
Rate
Time = Distance/Rate
cyclist travels away from home
17
x = speed?
17/x
cyclist returns home different route
22
x + 1
22/x+1
I know this is not correct and that I have to find the average rate. I also don't know the time.
Thank you in advance!

Answer by ankor@dixie-net.com(12701) (Show Source):
You can put this solution on YOUR website!
A cyclist bikes at a constant speed for 17 miles.
He then returns home at the same speed but takes a different route.
His return trip takes one hour longer and is 22 miles. Find his speed.
:
I would do it this way;
:
Let s = the constant speed
Then
= initial time out
and
= time to return
:
Write a time equation:
Time to return = initial time + 1 hr
= + 1
Multiply equation by s
22 = 17 + s
:
22 - 17 = s
:
s = 5 mph
:
Check solution by finding the times of each trip
22/5 = 4.4 hrs
17/5 = 3.4 hrs
-------------
diff = 1 hr