# A boat travelling at top speed upstream moves at 15 km per hour. When it travels downstream, again at top speed, it moves at 25 km per hour. What is the boat top speed in still water?

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Please help me this question is linear systems, and I think involves substitute. I would appreciate so much a quick detailed response. Thank you

Please help me this question is linear systems, and I think involves substitute. I would appreciate so much a quick detailed response. Thank you

##### 2 Answers

Let speed of boat in still water be

Let speed of stream be

Given

Upstream

#15=v_B-v_S# ...........(1)

Downstream#25=v_B+v_S# ...........(2)

Adding (1) and (2) to eliminate

#15+25=v_B-v_S+v_B+v_S#

#=>2v_B=40#

#=>v_B=40/2=20\ kmcdot h^-1#

#### Explanation:

Going up stream the boat is fighting the current. So

On the other hand, going down stream it is travelling with the current so

Its is all about 'relativity'. The boat is travelling at a constant speed in relation to just the water.

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Let the flow speed of the water in relation to land be

Let the boat speed in relation to water be

Going upstream the boat is fighting the current of the water.

So

Boat upstream related to land is

Boat downstream related to land is

For convenience drop the units of measurement for now

divide both sides by 2

Thus the boat speed in relation to water is