Help! How do you solve this?

Question

Its a math uniform motion problem.

The speed of a stream is 4 kph. A boat travels 6 km upstream in the same time it takes to travel 12km downstream. What is the speed of the boat in still water?

How to solve?? The correct equation will suffice

Answer 1

let v be the speed i still water

then

(v-4)*T = 6
(v+4)*T = 12

=> (v-4)/(v+4) = 6/12 .... etc

Answer 2

Vs = Stream Velocity [speed]= 4 km/h (down river)
Vb = Boat Vel. = ? (up river or down river => we will use different signals to show the direction)

Vu = Upstream Vel. = 4 - Vb [resultant speed]

Vd = Down stream Vel. = 4 + Vb [resultant speed]

Eq.:

X = Xo + V*t

where: X = total distance
Xo = 0 in this case
V = Velocity [speed]
t = time

The time to travel 6 km (X) up = T

X = Xo + V*t
6 = 0 + (4 - Vb)*T
1/T = (4 - Vb)/6 ==>(a)

The time to travel 12 km (X) down = T (the same time)

X = Xo + V*t
12 = 0 + (4 + Vb) * T
1/T = (4 + Vb)/12 ==>(b)

from (a) and (b):

(4 - Vb)/6= (4 + Vb)/12
4 - Vb = 4/2 + Vb/2
4 - 2 = Vb/2 + Vb
2 = 1.5Vb

Vb = 4/3 km/h

Testing the answer:
(a) 6 = 0 + (4 - Vb)*T
T = 6 / (4-4/3) = 6/8/3 = 9/4 hours = 135 min.

(b) 12 = 0 + (4 + Vb) * T
T = 12/(4+4/3) = 12/16/3 = 9/4 hours = 135 min.

Answer 3

X= distance
V=speed
T=time

X=VT

6=(V-4)T
12=(V+4)T

Divide the equations to get 2=(V+4)/(V-4)

2V-8 = V+4, so V=12