A boatman rows to a place 45 km distant and back in 20 hrs . he finds that he can row 12 km with stream in same time as 4 km against the stream. find the speed of stream.??

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A boatman rows to a place 45 km distant and back in 20 hrs . he finds that he can row 12 km with stream in same time as 4 km against the stream. find the speed of stream.??

Mathematics
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option are a.3km/hr b .2.5km/hr c.4 km/hr d.cant be determined.
Do you want the steps to get the answer or only the answer?
i need explantion too...

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Let's say without the stream he can go v_a and the stream goes v_b. Also let s = 45km and t = 20h. Then the statements are \[\frac{s}{v_a+v_b} + \frac{s}{v_a-v_b} = t\] and \[\frac{12km}{v_a+v_b} = \frac{4km}{v_a-v_b}\]
Solving the second condition you get \[v_a = 2v_b\] and substituting v_a in the first equation gives you \[3 km/h = \frac{4s}{3t} = v_b\]
hey am not the student of math ans thus i dont have much more idea of this...
so would u plz describe me in a simple way...
This is really the most simple way. Of course you should write the intermediate steps down for yourself. But all you have to do is use the definition that "speed = distance / time", modelize the given conditions into equations and do some algebraic reformulations.
Well.. My approach might be easier. If t_1 is the time needed to go with the stream, then the time to go against the stream is 3*t_1.
AnwarA: that knowledge must be gained from somewhere. And you only get it from the second equation.
Well I got it from the information that "he can row 12 km with stream in same time as 4 km against the stream".
I am just trying to simplify what you just did. I hope you don't mind :)
No, it's ok :-) But I must remark that dealing with these kind of relations in an intuitive way can lead to simple mistakes if the problems are getting more and more complicated, while doing it algebraic gives you much more mathematical rigour.
I totally agree. But since he didn't know how to use these mathematical equations, I though simplifying them would make them more meaningful to him, and it would help him get used to them. Anyway, he's gone :)

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