Problema Solution
The current in a stream moves at a speed of 5 km/h. A boat travels 14 km upstream and 14 km downstream in a total time of 15 hr. What is the speed of the boat in still water?
Answer provided by our tutors
let
v = the boats speed in still water, v>0
c = 5 km/h the speed of the current
d = 14 km
downstream speed: v + c
t1 = the time traveling downstream
upstream speed: v - c
t2 = the time traveling upstream
t1 + t2 = 15
since speed = distance/time
v + c = d/t1
v + 5 = 14/t1
t1 = 14/(v + 5)
v - c = d/t2
v - 5 = 14/t2
t2 = 14/(v - 5)
lets plug t1 and t2 in t1 + t2 = 15
14/(v + 5) + 14/(v - 5) = 15
by solving the equations we find and consider only the positive roots since v>0
v = 6.02 km/h
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the speed of the boat is 6.02 km/h.