Question 557452
Always start with the basic distance equation:  d = r*t, where d=distance, r=rate (or speed), and t=time.
s = speed in still water = 15 km/hr
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The current in the river may be defined as 'c'.
Going against the current, r = s-c, which means the current slows the boat down.
Going with the current, r = s+c, which means the current speeds the boat along.
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Going upstream (that is, against the current), the boat goes 15 km.
Going downstream  (that is, with the current), the boat goes 140 km.
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These distances are covered in the same time.
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d = r*t
so
t= d/r
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140 = (s+c) * t = (15+c)*t
35 = (s-c) * t = (15-c)*t
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140/(15+c) = t
35/(15-c) = t
t = t
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140/(15+c) = 35/(15-c)
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cross multiply
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140*(15-c) = 35*(15+c)
2100 - 140c = 525 + 35c
1575 = 175c
c = 1575/175
c = 9
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check this answer
t = 140/(15+9) = 140/24 = 35/6
t = 35/(15-9) = 35/6
t = t
correct
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Answer:  The river's current is 9 km/hr.
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Done.