SOLUTION: A motorboat takes 4 hours to travel 128 km going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the c

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Question 923643: A motorboat takes 4 hours to travel 128 km going upstream. the return trip takes 2 hours going downstream. what is the rate of the boat in still water and what is the rate of the current?
Answer by ptaylor(2198) (Show Source):
You can put this solution on YOUR website!
Distance(d) equals rate(r) times time(t) or d=rt; r=d/t and t=d/r
Let r=rate of boat in still water
And let c=rate of current
Now we know that upstream, the current subtracts from the boat's rate (r-c)
while downstream the current adds to the boat's rate (r+c)
Upstream (r-c)=128/4=32
r-c=32---eq1
Downstream
(r+c)=128/2=64
r+c=64---eq2
add eq 1 and eq2
2r=96
r=48 km/hr----rate of boat in still water
substitute r=48 in eq2:
48+c=64
c=64-48
c=16 km/hr---speed of current
CK
Upstream
4 hrs=128/(48-16)=128/32=4 hrs
Downstream
2 hrs=128/(48+16)=128/64=2 hrs
Hope this helps---ptaylor