College Algebra Question 2...Thank you sooo much!?

Question

A motorboat goes 8 miles upstream in the same amount of time it is able to go 12 miles downstream. The river flows at 3 miles per hour, what is the speed of the boat in still water.

Answer 1

Let the speed of the boat in still water be x.
v = s/t
In terms of time: t = s/v
t upstream = t downstream
speed upstream = x - 3 and speed downstream = x + 3
8 miles/ (x-3) = 12 miles / (x + 3)

solving for x:

12x - 36 = 8x + 24
4x = 60
x = 15 miles per hour. This is the speed of the boat in still water.

Answer 2

Read the question in such a way that it tells you how to set up the equation....
The time to go upstream 8 miles is equal to the time is takes to go down stream 12. The speed of the boat is constant

2 equations , 2 unknowns (time and speed)

first upstream
t(v-3)=8
where t is time, and v is velocity (speed), and - 3 because of direction of the boat

second down stream
t(v+3)=12

t=8/(v-3) & t=12/(v+3)

8/(v-3)=12/(v+3)

8v+24=12v-36
-4v=-60
v=15

Answer 3

Let
Vboat = velocity of boat in still water.
Tup = time to go upstream
Tdown = time to go down stream
Vriver = river speed = 3 mph

Time it takes to go upstream = distance / velocity, or
Tup = 8 miles / (Vboat - Vriver)

Time it takes to go downstream
Tdown = 12 / (Vboat + Vriver)

Sine the time upstream is the same as downstream, set the two equal to one another

8 / (Vboat - 3mph) = 12 / (Vboat + 3 mph)

Solve for Vboat

Vboat = 15 mph

Vbo

Answer 4

8=(v-3)*t
12=(v+3)*t

divide side by side

2/3=(v-3)/(v+3)

3v-9=2v+6

v=15 m/h (answer)