SOLUTION: A boat can go 20 km downstream in 2 hours. The return trip takes 5 hours. What would the speed of the boat be if there was no current? What is the speed of the current?

Question 515488: A boat can go 20 km downstream in 2 hours. The return trip takes 5 hours. What would the speed of the boat be if there was no current? What is the speed of the current?
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
d = r*t is the basic distance equation.
.
d = 20km
.
s = speed of the boat in calm water
c = speed of the current
so
r = s-c going upstream (against the current)
r = s+c going down stream (with the current)
.
Going downstream...
d/r = 2 hr
d/(s+c) = 2
20 = 2(s+c)
2(s+c) = 20
s+c = 10
.
Going upstream
d/r = 5 hr
d/(s-c) = 5
20 = 5(s-c)
5(s-c) = 20
s-c = 4
.
s + c = 10
s - c = 4
----------
2s = 14
s = 7 km/h
.
c = 10-s
c = 3 km/h
.
Check the distances
.
2 * (7+3) = 20 km
5 * (7-3) = 20 km
.
Answer: The boat can achieve 7 km/h in still water; the current is 3 km/h.
.
Done.
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