SOLUTION: Clark has a boat that can travel at 15kph in still water. It can go 140km with the current at the same time it takes to travel 35km against the current. what is the speed of the r

Question 557452: Clark has a boat that can travel at 15kph in still water. It can go 140km with the current at the same time it takes to travel 35km against the current.
what is the speed of the river??
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
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
.
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.
.
Going upstream (that is, against the current), the boat goes 15 km.
Going downstream (that is, with the current), the boat goes 140 km.
.
These distances are covered in the same time.
.
d = r*t
so
t= d/r
.
140 = (s+c) * t = (15+c)*t
35 = (s-c) * t = (15-c)*t
.
140/(15+c) = t
35/(15-c) = t
t = t
.
140/(15+c) = 35/(15-c)
.
cross multiply
.
140*(15-c) = 35*(15+c)
2100 - 140c = 525 + 35c
1575 = 175c
c = 1575/175
c = 9
.
check this answer
t = 140/(15+9) = 140/24 = 35/6
t = 35/(15-9) = 35/6
t = t
correct
.
Answer: The river's current is 9 km/hr.
.
Done.
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