a motorboat takes 4 hours to travel 256miles going up stream. the return trip takes 2 hrs going downstream. what is the the rate of the boat in still water and what is the rate current.

rate of the boat in still water = mi/hrs

rate of the current=mi/hrs.=

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

To solve this problem, we'll use the formula:

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.