SOLUTION: During the first part of a trip a conoeist travels 22 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at 5mph slower. The total time for the t

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: During the first part of a trip a conoeist travels 22 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at 5mph slower. The total time for the t      Log On

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Question 924458: During the first part of a trip a conoeist travels 22 miles at a certain speed. The canoeist travels 6 miles on the second part of the trip at 5mph slower. The total time for the trip is 3 hours.What is the speed for each part of the trip?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed in mi/hr fpr
the 1st part of the trip
Let +t+ = time in hrs for
the 1st part of the trip
---------------------
(1) +22+=+s%2At+
and
(2) +6+=+%28+s-5+%29%2A%28+3-t+%29+
------------------------
(2) +6+=+3s+-+15+-+s%2At+%2B+5t+
(2) +5t+-+s%2At+%2B+3s+=+21+
and
(1) +s+=+22%2Ft+
-------------------
(2) +5t+-+%2822%2Ft%29%2At+%2B+3%2A%2822%2Ft%29+=+21+
(2) +5t+-+22+%2B+66%2Ft+=+21+
(2) +5t%5E2+-+22t+%2B+66+=+21t+
(2) +5t%5E2+-+43t+%2B+66+=+0+
Use quadratic formula
+t+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+5+
+b+=+-43+
+c+=+66+
+t+=+%28-%28-43%29+%2B-+sqrt%28+%28-43%29%5E2+-+4%2A5%2A66+%29%29+%2F+%282%2A5%29+
+t+=+%28+43+%2B-+sqrt%28+1849+-+1320+%29%29+%2F+10+
+t+=+%28+43+%2B-+sqrt%28+529+%29%29+%2F+10+
+t+=+%28+43+-23+%29+%2F+10+
+t+=+2+
and
+3+-+2+=+1+
The speed for the 1st part is:
(1) +s+=+22%2Ft+
(1) +s+=+22%2F2+
(1) +s+=+11+ mi/hr
---------------------
The speed for the 2nd part is:
+s+-+5+=+6+ mi/hr
------------------
check:
(2) +6+=+%28+11-5+%29%2A%28+3-2+%29+
(2) +6+=+6%2A1+
and
(1) +22+=+s%2At+
(1) +22+=+11%2A2+
(1) +22+=+22+
OK