SOLUTION: I need help. I am having trouble setting up the equation. A cyclist rides a distance of 100 miles to a distant city. His return trip takes 3 hours longer because his speed decre

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Question 854011: I need help. I am having trouble setting up the equation.
A cyclist rides a distance of 100 miles to a distant city. His return trip takes 3 hours longer because his speed decreases by 30 mph. How fast did he ride each way?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = his speed riding to the city
+s-30+ = his speed returning
Let +t+ = his time in hours to get to the city
+t+%2B+3+ = his time returning
---------------------------------
Equation for 1st trip:
(1) +100+=+s%2At+
Equation for return trip
(2) +100+=+%28+s+-+30+%29%2A%28+t+%2B+3+%29+
-----------------------------
(2) +100+=+s%2At+-+30t+%2B+3s+-+90+
(2) +100+=+%28+t+%2B+3+%29%2As+-+30t+-+90+
(2) +%28+t+%2B+3+%29%2As+=+30t+%2B+190+
(2) +s+=+%28+30t+%2B+190+%29+%2F+%28+t+%2B+3+%29+
Substitute this result into (1)
------------------------------
(1) +100+=+%28+t%2A%28+30t+%2B+190+%29%29+%2F+%28+t+%2B+3+%29+
(1) +100t+%2B+300+=+30t%5E2+%2B+190t+
(1) +30t%5E2+%2B+90t+-+300+=+0+
(1) +t%5E2+%2B+3t+-+10+=+0+
I can see by looking at it, this is:
(1) +%28+t+%2B+5+%29%2A%28+t+-+2+%29+
+t+=+2+ ( because time is positive, not negative )
--------------------
+t+=+2+ hrs is his time to get to the city
+t+%2B+3+=+5+ hrs is his time to return
---------------
check:
(1) +100+=+s%2At+
(1) +100+=+s%2A2+
(1) +s+=+50+
and
(2) +100+=+%28+s+-+30+%29%2A%28+t+%2B+3+%29+
(2) +100+=+%28+s+-+30+%29%2A5+
(2) +20+=+s+-+30+
(2) +s+=+20+%2B+30+
(2) +s+=+50+
OK