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# A train travels from station A to station B. If it travels

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A train travels from station A to station B. If it travels [#permalink]  16 Sep 2012, 01:48
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A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Sep 2012, 01:55, edited 1 time in total.
Renamed the topic.
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Re: A train travels from station A to station B. If it travels [#permalink]  16 Sep 2012, 02:05
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Pansi wrote:
A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles

Let t be the usual time and x be the distance between A & B. So we need to find t and Distance x. The question gives us 2 combinations of speed & time, but the distance remains the same for both condition.

Equation 1 - x= 100 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.

Now equating 1 & 2 we get 100(t+.5)=120(t-.25)
=> 10t +5 = 12t - 3
=> 2t=8 => t= 4 hrs.
Hence x= 100(4+.5) =>100 X 4.5 => 450 miles.

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Re: A train travels from station A to station B. If it travels [#permalink]  16 Sep 2012, 04:06
Pansi wrote:
A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles

Let $$D$$ be the distance between the two stations A and B.
We can write directly the equation $$\frac{D}{100}=\frac{D}{120}+\frac{3}{4}$$, because at speed 100mph the train is late by half an hour, at 120mph is early by a quarter of an hour,
so the difference between the two times is +0.5 - (-0.25) = 0.75.
Solving for $$D$$ we obtain $$D=450$$ (now we already know that the answer is C) and the time is 450/100 - 0.5 = 4 hours.

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Re: A train travels from station A to station B. If it travels [#permalink]  23 Aug 2013, 03:29
Let D be the distance between the two stations A and B.
Equation 1, 100(T+.5)=D
Equation 2, 120(T-.25)=D
So, 100(T+.5)=120(T-.25)......Solving two equations, T=4
100(4+.5)=450
C is the correct ans.
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Re: A train travels from station A to station B. If it travels [#permalink]  29 Aug 2013, 08:01
T is the the scheduled time.
s1 = 100, t1 = t+30
s2 = 120, t2 = t-15
since speed varies inversely with time (when distance is kept constant). So if the speed ratio in the 2 cases is s1/s2 = 100/120 = 5/6, time taken in the 2 cases will be in the ratio t1/t2 = 6/5

(t+30)/(t-15) = 6/5
t = 240 mins = 4hrs
d=s*t = 100*4.5 = 450
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Re: A train travels from station A to station B. If it travels [#permalink]  26 Dec 2013, 05:02
Pansi wrote:
A train travels from station A to station B. If it travels at a speed of 100 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?

(A) 2 hours, 225 miles
(B) 3 hours, 350 miles
(C) 4 hours, 450 miles
(D) 5 hours, 550 miles
(E) 6 hours, 650 miles

Good question

100 (t+30) = 120 (t-15)
t = 240 minutes = 4 hours

Hope it helps
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Re: A train travels from station A to station B. If it travels [#permalink]  10 Nov 2014, 18:41
Distance = Speed * Time

t = ideal time

100 (t+30) = 120 (t - 15)

t = 240 = 4Hours

In the OA, had 4 hours been in more than one option, then distance would also required to be calculated
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Re: A train travels from station A to station B. If it travels   [#permalink] 10 Nov 2014, 18:41
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