Asteamboat went 8miles upstream in 1 hour. the return trip only took 30 minutes. assume that the speed and direction of the current was constant during both parts of the trip. find the speed of the boat in still water and the speed of the current.

recall your d = rt, distance = rate * time.

b = rate of the boat in still water

c = rate of the currrent

the distance going upstream is 8 miles, the distance going downstream is also the same 8 miles.

the boat took 1 hour going upstream, now, the boat is not going "b" mph fast, since it's going against the current, the current is eroding speed from, thus the boat going up is really going "b - c" fast.

likewise, when the boat goes downstream, is not going "b" fast either, is going faster because is going with the current and thus is really going "b + c" fast, and we know that trip back took 1/2 hour or 30 minutes.

the polynomial is a perfect square trinomial of the form a^2-2ab+b^2:

option a. true

step-by-step explanation:

9x^2-12x+4

comparing with the form a^2-2ab+b^2

1.) a^2=9x^2

solving for a: square root both sides of the equation:

sqrt(a^2)=sqrt(9x^2)

a=sqrt(9) sqrt(x^2)

a=3x

2.) b^2=4

solving for b: square root both sides of the equation:

sqrt(b^2)=sqrt(4)

b=2

to be a perfet square trinomial 2ab must be equal to 12x. let's check:

2ab = 2 (3x) (2)

2ab = 12x

correct