Question 1005354
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A boat travels 1 km upstream and 1 km back. The time for the round trip is 5 hrs. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?
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Let u will be an unknown speed of the boat in still water.
When boat moves upstream, its speed relative to the river bank is (u-4) {{{km/h}}}, and the time spent moving upstream is {{{1/(u-4)}}} hours. 
When boat moves downstream, its speed relative to the river bank is (u+4) {{{km/h}}}, and the time spent moving downstream is {{{1/(u+4)}}} hours. 
So, the total time upstream and downstream is {{{1/(u-4)}}} + {{{1/(u+4)}}} hours, and it is equal to 5 hours, according to the condition.
It gives you an equation

{{{1/(u-4)}}} + {{{1/(u+4)}}} = 5.

To solve it, multiply both sides by (u-4)*(u+4) and then simplify step by step. You will get

{{{(u+4)}}} + {{{(u-4)}}} = {{{5*(u^2 - 16)}}},

{{{5u^2 - 8u - 80}}} = {{{0}}}.

Apply the quadratic formula. The positive root is 4.205 {{{km/h}}} (approximately). 
The negative root doesn't work.

<U>Answer</U>. The speed of the boat in still water is 4.205 {{{km/h}}}.
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