Problema Solution
A boat travels 6 km upstream and 6 km back. The time for the
round trip is 4 hrs. The speed of the stream is 4km/hr. What
is the speed of the boat in still water?
Answer provided by our tutors
let
v = the speed of the boat in still water
t1 = the time of the downstream travel
t2 = the time of the upstream travel
s = 4 km/hr the speed of the stream
d = 6 km the distance traveled in one direction
we will use the formula distance = speed*time (since speed = distance/time)
the time for the round trip is 4 hrs
t1 + t2 = 4 => t2 = 4 - t1
the speed of the boat downstream is v + s = v + 4
t1(v + s) = d
t1(v + 4) = 6 = > t1 = 6/(v + 4)
the speed of the boat upstream is v - s = v - 4
t2(v - s) = d
t2(v - 4) = 6
plug t2 = 4 - t1 into the last equation
(4 - t1)(v - 4) = 6
next plug t1 = 6/(v + 4) into (4 - t1)(v - 4) = 6 we have
(4 - 6/(v + 4))(v - 4) = 6
by solving this equation we find and consider the positive roots since v>0
v = 5.77 km/hr
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the speed of the boat in still water is 5.77 km/hr.