math help?!?

Question

The letters A, B, R, T, V, and W are points on a line. T is the midpoint of AB, point R is the midpoint of AT and points V and W divide TB into three equal segments. If the length of VW is 1/4, then what is the length of segment RT.
a. 3/16
b. 3/8
c. 3/4
d.1
e. 17/16

Answer 1

The line

A R T V W B

VW=1/4

T is the mid point of AB, so AT=TB
V and W divide TB into 3 equal parts
so it follows that VW is 1/6 of AB.

Or AB = 6VW
We know that VW = 1/4
so AB = 6*(1/4) or 6/4

We know that T is the midpoint of AB,
so AT = (6/4)/2 or 6/8.

Finally, R is the midpoint of AT
So RT = (6/8)/2 or 6/16
We simplify and RT = 3/8.

Answer 2

If the length of AB is 24 units, then the other lengths are:
AT = TB = 12
AR = RT = 6
TV = VW = WB = 4
Therefore 4 units represent a length of 1/4.
RT is 6 units, and its length is (6/4)*(1/4) = 6/16 = 3/8.
Answer (b).