SOLUTION: A motorboat heads upstream a distance of 24 miles on a river with current running 3 miles per hour. The trip up and back takes 6 hours. Assuming the motorboat maintained a constant

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Question 739431: A motorboat heads upstream a distance of 24 miles on a river with current running 3 miles per hour. The trip up and back takes 6 hours. Assuming the motorboat maintained a constant speed relative to the water, what was it's speed?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The speed of the boat going upstream is
+s+-+3+ mi/hr
The speed of the boat going downstream is
+s+%2B+3+ mi/hr
where +s+ = the boat's speed in still water
Let +t+ = the time in hrs for the boat to go upstream
-----------------
Going upstream:
(1) +24+=+%28+s+-+3+%29%2At+
Going downstream:
(2) +24+=+%28+s+%2B+3+%29%2A%28+6+-+t+%29+
--------------------------
(2) +24+=+6s+%2B+18+-+s%2At+-+3t+
(2) +6s+-+s%2At+-+3t+=+6+
and
(1) +s%2At++=+3t+%2B+24+
-------------------
Substitute (1) into (2)
(2) +6s+-+3t+-+24+-+3t+=+6+
(2) +6t+=+6s+-+30+
(2) +t+=+s+-+5+
Substitute this back into (1)
(1) +24+=+%28+s+-+3+%29%2A%28+s-5+%29+
(1) +24+=+s%5E2+-+8s+%2B+15+
(1) +s%5E2+-+8s+-+9+=+0+
(1) +%28+s+-+9+%29%2A%28+s+%2B+1+%29+=+0+ ( by inspection )
+s+=+9+ ( can't use +s+=+-1+ )
The boats speed is 9 mi/hr without a current
check:
(1) +24+=+%28+9+-+3+%29%2At+
(1) +24+=+6t+
(1) +t+=+4+ hrs
and
(2) +24+=+%28+9+%2B+3+%29%2A%28+6+-+t+%29+
(2) +24+=+12%2A%28+6+-+t+%29+
(2) +24+=+72+-+12t+
(2) +12t+=+72+-+24+
(2) +12t+=+48+
(2) +t+=+4+ hrs
OK