SOLUTION: 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?

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) , and the time spent moving upstream is  hours. 
When boat moves downstream, its speed relative to the river bank is (u+4) , and the time spent moving downstream is  hours. 
So, the total time upstream and downstream is  +  hours, and it is equal to 5 hours, according to the condition.
It gives you an equation

 +  = 5.

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

 +  = ,

 = .

Apply the quadratic formula. The positive root is 4.205  (approximately). 
The negative root doesn't work.

Answer. The speed of the boat in still water is 4.205 .

With S being speed of boat in still water, time equation formed is: , resulting in the quadratic equation: 

This CANNOT be factored, so use the quadratic equation formula, or completing the square to solve for S

Solve for S to get a positive (> 0) solution, or speed of:  km/h in still water