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?

Question 1005354: 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?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52834) (Show Source): You can put this solution on YOUR website!
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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) , 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 .

MathTherapy, thank you for your support!

Answer by MathTherapy(10555) (Show Source): You can put this solution on YOUR website!
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?

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
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