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The Middlebury train station is between the Appleton and Lancaster sta

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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
y/35=y/55+1/2, can anyone please explain how to arrive at this equation?
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The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
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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!
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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
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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The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
chetan2u
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
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

I think it will be that " the distance between M and L is twice the distance between M and A."
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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
(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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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
chetan2u
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
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

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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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
brains
chetan2u
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
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

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?

No, you are correct.
Corrected the typo. Thanks
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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
chetan2u
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
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

Hi chetan2u, could you elaborate on how do you derive y = x/2 bit please? Thanks
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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
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Re: The Middlebury train station is between the Appleton and Lancaster sta [#permalink]
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