Problema Solution
In still water Derek can paddle his canoe at 6.5 km/h. On a river the canoe travels faster downstream than upstream because of the current. In the morning Derek travels upstream and takes 5 hours and then in the afternoon Derek travels downstream the same distance and takes 2 hours. What is the speed of the current? Answer to the nearest tenth.
Answer provided by our tutors
let
v = 6.5 km/h the rate in still water
c = the rate of the current
t1 = 5 hr the time of the travel against the current (upstream)
t2 = 2 hr the time of the travel with the current (downstream)
the rate of the canoe traveling upstream is: v - c
the rate of the canoe traveling downstream is: v + c
since the rate = distance/time => distance = time*rate
traveling upstream:
d = t1(v - c)
d = 5(6.5 - c)
traveling downstream:
d = t2(v + c)
d = 2(6.5 + c)
by solving the equation:
5(6.5 - c) = 2(6.5 + c)
we find:
c = 2.8 km/h
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the speed of the current is 2.8 km/h.