SOLUTION: The sped of the current in the Mississippi River is 5mph. A boat travels downstream 26 miles and returns in a total of 32/3 hours. What is the speed of the boat in still water.

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Question 1008924: The sped of the current in the Mississippi River is 5mph. A boat travels downstream 26 miles and returns in a total of 32/3 hours. What is the speed of the boat in still water.
Any help is desperately needed as soon as possible.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +s+ = the speed of the boat in still water
+s+%2B+5+ = the speed of the boat going downstream
+s+-+5+ = the speed of the boat going upstream
Let +t+ = time in hrs for the boat to go downstream
+11%2F3+-+t+ = time in hrs for the boat to go upstream
---------------------------------------------
Equation for going downstream:
(1) +26+=+%28+s%2B5+%29%2At+
Equation for going upstream:
(2) +26+=+%28+s-5+%29%2A%28+11%2F3+-+t+%29+
--------------------------
(2) +26+=+%2811%2F3%29%2As+-+55%2F3+-+s%2At+%2B+5t+
(2) +26+=+%2811%2F3%29%2As+-+55%2F3+-+%28+s+-+5+%29%2At+
and
(1) +t+=+26%2F+%28+s%2B5+%29+
By substitution:
(2) +26+=+%2811%2F3%29%2As+-+55%2F3+-+%28+s+-+5+%29%2A%28+26%2F%28+s%2B5+%29+%29+
Multiply both sides by +3%2A+%28+s+%2B+5+%29+
(2) +78%2A%28+s%2B5+%29+=+11s%2A%28+s%2B5+%29+-+55%2A%28+s%2B5+%29+-78%2A%28+s-5+%29+
(2) +78s+%2B+390+=+11s%5E2+%2B+55s+-+55s+-+275+-+78s+%2B+390+
(2) +11s%5E2+-+156s+-+275+=+0+
Use quadratic formula
+s+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+11+
+b+=+-156+
+c+=+-275+

+s+=+%28+156+%2B-+sqrt%28+24336+%2B+12100+%29%29+%2F+22+
+s+=+%28+156+%2B-+sqrt%28+36436+%29%29+%2F+22+
+s+=+%28+156+%2B+190.882+%29+%2F+22+
+s+=+15.767+ mi/hr
The speed of the boat in still water is 15.767 mi/hr
check:
(1) +26+=+%28+s%2B5+%29%2At+
(1) +26+=+%28+15.767%2B5+%29%2At+
(1) +26+=+20.767t+
(1) +t+=+1.252+
and
(2) +26+=+%28+s-5+%29%2A%28+11%2F3+-+t+%29+
(2) +26+=+%28+15.767-5+%29%2A%28+11%2F3+-+t+%29+
(2) +11%2F3+-+t+=+26%2F10.767+
(2) +3.667+-+t+=+2.415+
(2) +t+=+1.252+
OK
This seems to check out -you could still get
another opinion, but I think my method is OK