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

rate of the boat in still water=mi/hr
rate of the current=mi/hr

rate in still water --- x mph

raate of current ---- y mph

#1: 4(x-y) = 256
x-y = 64

#2: 2(x+y) = 256
x+y = 128

add them .....

I will let you finish, let me know what you get.

(BTW, the rates seem very unreasonable as you will see)

8...? not sure..

96...? ahah..

still unsure.

To find the rate of the boat in still water and the rate of the current, we can use the formula:

Rate of boat in still water = (Rate downstream + Rate upstream) / 2
Rate of current = (Rate downstream - Rate upstream) / 2

Let's calculate the rates:

Given that the boat takes 4 hours to travel 256 miles upstream:
Rate upstream = Distance / Time = 256 miles / 4 hours = 64 mi/hr

Given that the boat takes 2 hours to travel 256 miles downstream:
Rate downstream = Distance / Time = 256 miles / 2 hours = 128 mi/hr

Now we can substitute the values into the formulas:

Rate of boat in still water = (128 mi/hr + 64 mi/hr) / 2 = 192 mi/hr / 2 = 96 mi/hr

Rate of current = (128 mi/hr - 64 mi/hr) / 2 = 64 mi/hr / 2 = 32 mi/hr

Therefore, the rate of the boat in still water is 96 mi/hr, and the rate of the current is 32 mi/hr.