SOLUTION: The current in a stream moves at a speed of 3km/h. A boat travels 40 km upstream and 40 km downstream in a total time of 14 hours. What is the speed of the boat in still water?

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Question 591146: The current in a stream moves at a speed of 3km/h. A boat travels 40 km upstream and 40 km downstream in a total time of 14 hours. What is the speed of the boat in still water?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+s+-+c+ = speed of boat going upstream
+s+%2B+c+ = speed of boat going downstream
Let +t+ = time going downstream
given:
+c+=+3+ km/hr
Going downstream:
(1) +40+=+%28+s+%2B+3+%29%2At+
Going upstream:
(2) +40+=+%28+s+-+3+%29%2A%28+14+-+t+%29+
-------------------------
(1) +s+%2B+3+=+40%2Ft+
(1) +s+=+40%2Ft+-+3+
and
(2) +40+=+%28+40%2Ft+-+3+-+3+%29%2A%28+14+-+t+%29+
(2) +40+=+%28+40%2Ft+-+6+%29%2A%28+14+-+t+%29+
(2) +40+=+560%2Ft+-+84+-+40+%2B+6t+
(2) +6t+%2B+560%2Ft+=+164+
(2) +6t%5E2+%2B+560+=+164t+
(2) +3t%5E2+-+82t+%2B+280+
+t+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+3+
+b+=+-82+
+c+=+280+
+t+=+%28+-%28-82%29+%2B-+sqrt%28+%28-82%29%5E2+-+4%2A3%2A280+%29%29+%2F+%282%2A3%29+
+t+=+%28+82+%2B-+sqrt%28+6724+-+3360+%29%29+%2F+6+
+t+=+%28+82+%2B-+sqrt%28+3364+%29%29+%2F+6+
+t+=+%28+82+%2B+58%29+%2F+6+
+t+=+140%2F6+
+t+=+23.333+ too big
+t+=+%28+82+-+58%29+%2F+6+
+t+=+24%2F6+
+t+=+4+
and
(1) +s+=+40%2Ft+-+3+
(1) +s+=+40%2F4+-+3+
(1) +s+=+10+-+3+
(10 +s+=+7+
The speed of the boat in still water is 7 km/hr
check:
(2) +40+=+%28+s+-+3+%29%2A%28+14+-+t+%29+
(2) +40+=+%28+7+-+3+%29%2A%28+14+-+4+%29+
(2) +40+=+4%2A10+
(2) +40+=+40+
OK