Problema Solution
The current in a stream moves at a speed of 3 km/h. A boat travels 55 km upstream and 55km downstream in a total time of 16hr. Complete the following table. What is the speed of the boat in still water.
d r t
Upstream ___ r-3 t1
Downstream 55 ____ t2
Total time __
Answer provided by our tutors
let
c = 3 km/h the speed of the current
v = the speed of the boat in still water, v=>0
d = 55 km the distance traveled in each direction
traveling upstream the speed of the boat is: v - c
the time of the trip upstream is: d/(v - c)
traveling downstream the speed of the boat is: v + c
the time of the trip downstream is: d/(v + c)
The total time is 16 hours or:
d/(v - c) + d/(v + c) = 16
55/(v - 3) + 55/(v + 3) = 16
by solving we find:
v = 8 km/h
click here to see the step by step solution of the equation:
the speed of the boat in still water is 8 km/h.