A train trip begins at Lawrenceville, makes stops first at Milton and

L---------M---------O----------P
If OP=x, then LO=4x
If LM=y, then MO=2y
But LO=4x=3y, hence y=4x/3
MP=2y+x = 8x/3 +3x/3 = 11x/3

We are to determine LO/MP = 4x/(11x/3) = 12/11

The answer is D.

given
LO= 4OP
LM=1/2 MO
LO= MP *x
x to be determined
let
OP = 1
so
LO = 4
and LM = 4/3 and MO = 8/3
so MP = 8/3+ 1 ; 11/3
4= 11/3 *x
x = 12/11
IMO D




A train trip begins at Lawrenceville, makes stops first at Milton and then at Overton, and ends at Pottstown. The distance between Lawrenceville and Overton is four times the distance between Overton and Pottstown, and the distance between Lawrenceville and Milton is equal to half the distance between Milton and Overton. The trip from Lawrenceville to Overton is how many times the trip from Milton to Pottstown?

A. 1/3
B. 11/12
C. 1
D. 12/11
E. 4/3

A train trip begins at Lawrenceville, makes stops first at Milton and then at Overton, and ends at Pottstown. The distance between Lawrenceville and Overton is four times the distance between Overton and Pottstown, and the distance between Lawrenceville and Milton is equal to half the distance between Milton and Overton. The trip from Lawrenceville to Overton is how many times the trip from Milton to Pottstown?

A. 1/3
B. 11/12
C. 1
D. 12/11
E. 4/3

Let distance between Overton and Pottstown = x
Then distance between Lawrenceville and Overton = 4x
Now, distance between Milton to Overton = y
Then distance Lawrenceville to Milton = \(\frac{y}{2}\)

So, \(\frac{y}{2}\) + y = 4x
\(\frac{8}{3}x\) = y

Now, \(\frac{4x }{ y + x}\) = \(\frac{4x}{(8/3x) + x}\)
= 12/11

Answer D.

The train trip from L -> M -> O -> P => LM + MO + OP = LP
The distance between Lawrenceville and Overton is four times the distance between Overton and Pottstown
\(=> LO = 4OP => LO = \frac{4}{5} LP; OP = \frac{1}{5}LP \)
The distance between Lawrenceville and Milton is equal to half the distance between Milton and Overton
\(=> 2LM = MO => MO = \frac{2}{3}LO = \frac{8}{15}LP\)
\(=> MP = MO + OP = \frac{8}{15}LP + \frac{1}{5}LP = \frac{11}{15}LP\)
\(=> \frac{LO}{MP} = \frac{4}{5}:\frac{11}{15}= \frac{12}{11}\) => Choice D

L>M>O>P
LO=4OP
LM=MO/2

LO=LM+MO=MO/2+MO=x/2+x=3x/2

OP=LO/4=(MO/2+MO)/4
MP=MO+OP=MO+(MO/2+MO)/4=x+(3x/8)=11x/8

LO/MP=(3x/2)/(11x/8)=3x/2*8/11x=12/11

Ans (D)

let
L-M be y
M-Y becomes 2y
L-O be 4x
O-P is x

from above 4x=3y
y=4x/3
so we have to find what is z in L-O=z(M-P)=z(2y+x)=z(8x/3+x)= z(11x/3)....but L-O=4x=12x/3

so z=12/11

OA:D