speed upstream=256/4=64
speed downstream=256/2=128
rate of boat=128+64/2=96mi/hrs
rate of current=128-64/2=32mi/hrs
rate of the boat in still water = mi/hrs
rate of the current=mi/hrs.=
speed downstream=256/2=128
rate of boat=128+64/2=96mi/hrs
rate of current=128-64/2=32mi/hrs
rate = distance / time
Let's assign variables to the unknowns:
Let's say the rate of the boat in still water is represented by "b" (mi/hr), and the rate of the current is represented by "c" (mi/hr).
1. Going upstream:
Given that it takes 4 hours to travel 256 miles, we can use the formula:
b - c = 256 / 4
2. Going downstream:
Given that it takes 2 hours to travel 256 miles, we can use the formula:
b + c = 256 / 2
Now we have a system of two equations:
1. b - c = 64 (equation 1)
2. b + c = 128 (equation 2)
To solve this system of equations, we can use the method of elimination. By adding equation 1 and equation 2, the "c" term will be eliminated:
(b - c) + (b + c) = 64 + 128
2b = 192
Divide both sides of the equation by 2:
b = 96
So the rate of the boat in still water is 96 mi/hr.
Substituting this value back into either of the original equations, we can solve for the rate of the current.
Using equation 2: b + c = 128
96 + c = 128
Subtract 96 from both sides of the equation:
c = 32
So the rate of the current is 32 mi/hr.