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There's a boat traveling on a river. When it's going with the river flow, it takes 10 minutes to cover 1km, but when going against the flow, it takes it 15 minutes.

How long does it take to cover 1km when traveling in still water?

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closed as off-topic by manshu, AJL, CodeNewbie, Deusovi♦, JonTheMon Mar 4 '16 at 13:53

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is off-topic as it appears to be a mathematics problem, as opposed to a mathematical puzzle. For more info, see "Are math-textbook-style problems on topic?" on meta." – manshu, AJL, CodeNewbie, Deusovi, JonTheMon
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ This is math homework. :( $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:20
  • $\begingroup$ @PiotrPytlik Hah. No. This is easy but tricky question ;) $\endgroup$ – neiiic Mar 4 '16 at 10:21
  • $\begingroup$ please tell me how this is a tricky question? according to the accepted answer, it's a basic math problem, like i said :P $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:42
  • $\begingroup$ @PiotrPytlik I'm new here. I think it's be interesting. Some people say 12.5, what is wrong. $\endgroup$ – neiiic Mar 4 '16 at 10:43
  • $\begingroup$ Sorry that i was rude, I do that sometimes. Good luck with future puzzles. $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:49
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The boat takes 12 min to cover 1km in still water.

Going downstream, the boat is moving at 6km/hr. Going upstream, it moves at 4km/hr. The difference is twice the speed of the river, which is flowing at 1km/hr.

So, the boat itself moves at 5km/hr in still water.

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    $\begingroup$ Well well well. So i guess it really was math homework. $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:38
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Answer:

It will never travel 1km in still water

Explanation

A river will never have still water, as a river by definition is a stream of water that flows into a larger body (a lake, or sea etc). Therefore it will never be still

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  • $\begingroup$ as far as this could be the correct answer, i think perhaps the question doesn't refer to the boat still being in the river. $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:30
  • $\begingroup$ Boat can travel with motor. Soo that moving. $\endgroup$ – neiiic Mar 4 '16 at 10:31
  • $\begingroup$ It refers to the boat travelling in still water. This is impossible on a river as the question states. Regardless of whether the boat has a sail, engine, motor, jet engine etc the river will never have still water, and so this situation will never happen $\endgroup$ – Lynch Mar 4 '16 at 10:31
  • $\begingroup$ @Lynch notice how he didn't actually say "travelling in the river when it's still", but he said "in still water"... a lake is still water, and it doesn't violate the rules. $\endgroup$ – Piotr Pytlik Mar 4 '16 at 10:32
  • $\begingroup$ You're not wrong, I can accept that one lol good point $\endgroup$ – Lynch Mar 4 '16 at 10:45
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Let x be the speed of boat and y be the speed of river flow.

Then

(x+y)*10 = 1

(x-y)*15 = 1

That is

(x+y)10 = (x-y)*15

which gives 

y = x/5

No consider t be the time it will take to cover 1Km in still water.

Then 

(x+y)*10 = x*t  

(x+x/5)*10 = x*t

60x/5x = t

So we get t = 12

The boat will take 12 minutes to cover 1Km in still water.

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let's calculate step by step

  1. Going downstream: 1/(10/60) Km/hr => 6Km/hr
  2. Going upstream 1/(15/60) km/hr => 4 Km/hr

Downstream equation: speed of boat + speed of current = x + Y = 6

upstream equation: speed of boat - speed of current = x - Y = 4

On solving these two equations: speed of boat = 5Km/hr And thus it will take (1/5)hr or 12 mins to cover 1Km in still water.

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