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A boat goes upstream for 3 hours and then downstream for the same time. If the speed of the current is 3.5 kmph, how far from its original position is the boat now?

Speed of boat in still water = X

Speed of stream = Y

Upstream speed = X – 3.5

Downstream speed = X + 3.5

[enter image description here][1]

I am stuck here. How to calculate the extra distance that boat has traveled?


After seeing Ross's answer: What does 21 mean?

I draw two possibilities of 21 km in this diagram:

[enter image description here][1]

[1]: https ://i.stack.imgur.com/4gRlP.jpg

[1]: https ://i.stack.imgur.com/SZEkt.jpg

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  • $\begingroup$ How far does the boat travel in $3$ hours when it is going upstream? Downstream? $\endgroup$ – saulspatz Nov 16 '19 at 1:46
  • $\begingroup$ @saulspatz upstream distance = (X – 3.5)3. Downstream distance = (X + 3.5)3. $\endgroup$ – Scott Kooper Nov 16 '19 at 2:12
  • $\begingroup$ I can't see either of the new images you link to. $21$ km is the distance the water travels downstream in $6$ hours relative to the shore. I claim that the boat is in the same position relative to the water after the journey, so it also has moved $21$ km relative to the shore. $\endgroup$ – Ross Millikan Nov 16 '19 at 4:18
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This is a trick question. Note that you are not given the boat speed in still water, which is because you don't need it. You can do everything relative to the water. It goes one direction for $3$ hours, then the other direction for $3$ hours, so relative to the water it is back where it started. In $6$ hours the water has moved $6 \cdot 3.5=21$ km.

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  • $\begingroup$ Sorry but this looks wrong. The boat cannot be back where it started because it covers less distance upstream and more distance downstream. Am I overlooking something?.. $\endgroup$ – AgentS Nov 16 '19 at 2:01
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    $\begingroup$ @pooja What you say is correct, but you are looking at the position of the boat relative to the ground, whereas Ross specifically says he is talking about the position relative to the water. In $6$ hours, the water moves $21$ km downstream, so the boat is $21$ km downstream, relative to the ground. $\endgroup$ – saulspatz Nov 16 '19 at 2:28
  • $\begingroup$ Ahh I get it XD relative to the water the displacement of boat is $0$ as it's speed relative to water is same in both directions. Awesomess! $\endgroup$ – AgentS Nov 16 '19 at 2:36
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The boat moves $3X-10.5$ km upstream, as you said. It then moves $3X+10.5$ km downstream, as you also said. If we say that upstream is the positive direction, and the boat starts from $0$, the the boat's position is $$3X-10.5-(3X+10.5)=-21.$$ That is, the boat is $21$ km downstream from where it started.

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