The Middlebury train station is between the Appleton and Lancaster sta

The Middlebury train station is between the Appleton and Lancaster stations and all three are serviced by the same track. What is the distance between Middlebury and Lancaster?


(1) If a train can travel 50 miles on one pound of coal, it will use twice as much coal traveling from MiddleBury to Lancaster as it will use to travel between Middlebury and Appleton.
This tells us that the distance between M and L is twice the distance between M and A
A....x....M……..2x……..L
But nothing about x
insuff

(2) Traveling from Appleton to Middlebury at an average rate of 35 mph takes 30 minutes longer than at an average rate of 55 mph.
Let the distance between A to M be y, so \(\frac{y}{35}=\frac{y}{55}+\frac{1}{2}\)
we will get value of y from here that is the distance between A and M
BUt nothing about distance between M and L
insuff

combined
y=x/2 or x=2y and we will know y from statement II
distance between M and L \(= 2y\)
sufficient as we know what is y

C
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Questions involving distance will likely be based either on the speed*time=distance equation or some kind of ratio/subtraction between the whole (Appleton-Lancaster) and its parts (Appleton-Middlebury, Middlebury-Lancaster).
We'll look for these pieces of information, a Logical approach.

(1) This gives us the ratios between the distances, not exact numbers.
Insufficient.

(2) This lets us calculate the Appleton-Middlebury distance (as we can create an equation with 1 variable) which is insufficient on its own.
Insufficient.

Combined:
(2) gives us the Appleton-Middlebury distance and (1) gives us the ratio between the Appleton-Middlebury to Middlebury- Lancaster distances.
Sufficient!

(C) is our answer.

y/35=y/55+1/2, can anyone please explain how to arrive at this equation?

Hello!

The speeds are given in miles per hour. So, from statement 2, the 30 minutes is converted into \(\frac{1}{2}\) hours.

And we know that \(Time = \frac{Distance}{speed}\).

So,
Time taken to travel at 35 mph = Distance/35.
Time taken to travel at 55 mph = Distance/55.

Now, travelling at 35 mph takes 30 mins more than travelling at 55 mph.
Therefore,
\(\frac{D}{35} = \frac{D}{55} +\frac{1}{2}\)
Cheers!

Thanks ohsostudiousMj, that sums it up quite well. I was missing out that the time units are in hour, hence 1/2 (30mins).

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I think it will be that " the distance between M and L is twice the distance between M and A."
chetan2u VeritasKarishma

(1) Gives us ratios. We know the distance between M and L is twice the distance between A and M. However, we only know ratios -- we are not able to determine a figure.

(2) Gives us the distance of A to M. However we don't know the ratio of A to M vs M to L.

(1 and 2) We are able to determine the distance of A to M and M to L.
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Hi, chetan2u

Does not statement A says that distance between M and L is twice the distance between A and M. Am I wrong to interpret?
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No, you are correct.
Corrected the typo. Thanks
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Hi chetan2u, could you elaborate on how do you derive y = x/2 bit please? Thanks

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