SOLUTION: a barge move 6km/h in still water. it travels 15 km upstream and 15 km downstream in a total time of 9 h. what is teh speed of the current
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Question 513707: a barge move 6km/h in still water. it travels 15 km upstream and 15 km downstream in a total time of 9 h. what is teh speed of the current
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Time equals distance divided by rate. The downstream rate is 
where 
is the speed of the current. The upstream rate is 
. If we let 
represent the amount of time to go downstream, then 
must represent the amount of time to go upstream.
Downstream trip:
Upstream trip:
Substituting:
Then:
The lowest common denominator is the product of the two conjugate denominators, hence the difference of two squares:
\ +\ 15(6\ -\ r_c)\ =\ 9(36\ -\ {r_c}^2))
A little Algebra Music, Maestro (verification left as an exercise for the student):
Solve for . Discard the negative root.
John
My calculator said it, I believe it, that settles it
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