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.

(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.
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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 A is twice the distance between M and L
A....-2x-....M..-x-..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.
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=2x= we will know y from statement II
distance between M and L \(= \frac{y}{2}\)
sufficient as we know what is y

C
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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!
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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