SOLUTION: The speed of the current in a river is 5 miles per hour. A boat leaves a dock on the bank of the river, travels upstream 25 miles, and returns to the dock in 12 hours. What is th

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Question 729969: The speed of the current in a river is 5 miles per hour. A boat leaves a dock on the bank of the river, travels upstream 25 miles, and returns to the dock in 12 hours. What is the speed of the boat in still water?
Found 2 solutions by lynnlo, Finavon:
Answer by lynnlo(4176) About Me  (Show Source):
Answer by Finavon(81) About Me  (Show Source):
You can put this solution on YOUR website!
+Time+=+Distance%2FSpeed+
Boat speed: x mph
Total time = 25%2F%28x-5%29+%2B+25%2F%28x%2B5%29+=+12+
Multiply by (x-5)*(x+5)
25*(x+5) + 25*(x-5) = 12*(x-5)*(x+5)
+50x+=+12x%5E2+-+12%2A25+
+12x%5E2+-+50x+-+300+=+0+
+6x%5E2+-+25x+-+150+=+0+
Solves for +x+=+%2825+%2B-sqrt%2825%5E2+-4%2A6%2A%28-150%29%29%29%2F%282%2A6%29+
+x+=+%2825+%2B-sqrt%28625%2B3600%29%29%2F12+
Real x = 90/12 = 7.5 mph
Check:
25 miles @ 2.5 mph 10 hrs
25 miles @ 12.5 mph 2 hours
Total 12 hrs