Problema Solution
a boat travels 80 miles downstream with the current in 4 hours and returns to the starting point going against the current in 5 hours. Find the speed of the current and the speed of the boat in still water.
Answer provided by our tutors
Let
c = the speed of the current
v = the speed of the boat in still water
d = 80 mi the distance traveled in each direction
Traveling downstream the speed of the boat is: v + c
Traveling upstream the speed of the boat is: v - c
Since distance = speed*time we have:
(v + c)*4 = d
(v - c)*5 = d
We plug the value for d = 80 mi and get the following system of equations:
(v + c)4 = 80
(v - c)5 = 80
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click here to see the system of equations solved for c and v
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v = 18 mph
c = 2 mph
The speed of the current is 2 mph.
The speed of the boat in still water is 18 mph.