SOLUTION: during th first part of a trip a canoeist travels 37 miles at a certain speed. the canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower the total ti

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Question 617203: during th first part of a trip a canoeist travels 37 miles at a certain speed. the canoeist travels 22 miles on the second part of the trip at a speed of 5 mph slower the total time for the trip is 3 hrs. what was the speed on each part of the trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let t = the time for the 1st trip
+3+-+t+ = time for the 2nd trip
Let +s+ = the speed for the 1st trip
+s+-+5+ = the speed for the 2nd trip
-------------------
Ist rip:
(1) +37+=+s%2At+
2nd trip:
(2) +22+=+%28+s+-+5+%29%2A%28+3+-+t+%29+
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(2) +22+=+3s+-+15+-+s%2At+%2B+5t+
From (1):
+t+=+37%2Fs+
(2) +22+=+3s+-+15+-+s%2A%2837%2Fs%29+%2B+5%2A%2837%2Fs%29+
Multiply both sides by +s+
(2) +22s+=+3s%5E2+-+15s+-+37s+%2B+185+
(2) +3s%5E2+-+52s+-+22s+%2B+185+=+0+
(2) +3s%5E2+-74s+%2B+185+=+0+
Use quadratic formula to solve for +s+