A motorboat travels 165 kilometers in 3 hours going upstream. It travels 207 kilometers going downstream in the same amount of time. What is the rate of the boat in still water and what is the rate of the current?

Step-by-step explanation:

b = the speed of the boat in still water.

S = the speed of the stream

Relative to the bank, the speed upstream is B-S.

The speed downstream is B+S.

Use the equation for distance.

Rate * Time = Distance

Upstream

(B-S)6 = 258

(B+S)6 = 330

Simplify first:

B-S = 43

B+S = 55

Solve by elimination. Add the two equations.

2B = 98

B = 49 mi/hr

Substitute this into either equation and solve for S.

B+S = 55

49+S = 55

S = 6 mi/hr

f(2x−x2)=−3x2+6x−1

step-by-step explanation:

set up the composite function and evaluate.

f(2x−x2)=−3x2+6x−1