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Train A left Centerville Station, heading toward Dale City Station, at

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Bunuel
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Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   27 Dec 2015, 09:38
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Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.
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C
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BrentGMATPrepNow
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Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   Updated on: 01 Apr 2020, 05:32
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Bunuel wrote:
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.


3:00pm - Train A (traveling 30 miles per hour) left Centerville Station, heading toward Dale City Station
If the train travels 30 miles EVERY HOUR, then it travels 10 miles every 20 minutes (since 20 minutes = 1/3 hours)
In other words, at 3:20pm, Train A has already traveled 10 miles.
So, at 3:20, the trains are now 80 miles apart.

3:20pm - Train B (traveling 10 miles per hour) left Dale City Station heading toward Centerville Station
At this point (at 3:20pm), the trains are 80 miles apart.
Also, every hour, Train A moves 30 miles toward train B, and Train B moves 10 miles towards train A. This means the gap between them is decreasing at a rate of 40 miles per hour.

At this rate, the 80-mile gap will be reduced to zero miles (i.e., the trains meet) in 2 hours.

So, the trains will meet at 3:20pm + 2 hours = 5:20pm

Answer: C

Originally posted by BrentGMATPrepNow on 25 Apr 2018, 17:50.
Last edited by BrentGMATPrepNow on 01 Apr 2020, 05:32, edited 1 time in total.
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   27 Dec 2015, 10:16
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the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 3:20 +2=5:20

Hence answer is C.Hope i am correct
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   29 Dec 2015, 06:00
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kplusprinja1988 wrote:
the distance travelled by the train A in first 20 minutes will be 10.
The distance which will be remaining is 80.
Now both trains are running in opposite direction.Their speed will be added so 40.
Time at which they will meet =80/40=2
time of train B will be 3:20 +2=5:20

Hence answer is C.Hope i am correct





as per the question
train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m
and
Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m
Distance between the two stations = 90 miles
speed of train A =30 mile per hour
speed of train B =10 mile per hour
Relative speed = 40 mile per hour(since they are travelling in opposite direction)
relative distance = 90 -(distance travelled by train A in 20 minutes)
= 90 -10 = 80 miles
thus time taken = 80/40=2 hours from 3:20 pm =5:20 pm
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   13 Aug 2017, 20:24
Bunuel wrote:
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.


Bunuel okay one thing I don't like about this question that I was hoping you could clear up- I came up with the original formula at first

Distance traveled by A + Distance traveled by B = Length between Centerville and Dale

A =30 (x +20)
B= 10(x)

30x +600 + 10x = 90 - this obviously didn't seem right but in another similar problem they expressed the equation this way? Like instead of below where I write 30(x +1/3) they put the actual amount of minutes? How do we distinguish? Do we just intuitively pick smart numbers?

A= 30(x + 1/3)
B = 10(x)

30x + 10 + 10x =90
40x= 80
x= 2 hours

2 hours + 20 minutes=

C
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   14 Aug 2017, 00:55
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Nunuboy1994 wrote:
Bunuel wrote:
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.


Bunuel okay one thing I don't like about this question that I was hoping you could clear up- I came up with the original formula at first

Distance traveled by A + Distance traveled by B = Length between Centerville and Dale

A =30 (x +20)
B= 10(x)

30x +600 + 10x = 90 - this obviously didn't seem right but in another similar problem they expressed the equation this way? Like instead of below where I write 30(x +1/3) they put the actual amount of minutes? How do we distinguish? Do we just intuitively pick smart numbers?

A= 30(x + 1/3)
B = 10(x)

30x + 10 + 10x =90
40x= 80
x= 2 hours

2 hours + 20 minutes=

C


30 and 10 are rates in miles per hour, so in (rate)(time) = (distance), the (time) must also be in in hours, the same way x above is the number of hours, not minutes.
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   18 Aug 2017, 09:05
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Bunuel wrote:
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.


Since 20 minutes = 1/3 hour, we can let the time of Train B = t hours, and thus Train A = t + 1/3 hours.

The distance for Train A is 30(t + 1/3) = 30t + 10, and the distance for train B is 10t; thus:

30t + 10 + 10t = 90

40t = 80

t = 2 hours

So, the trains passed each other at 3:20 + 2 hours = 5:20 p.m.

Answer: C
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   21 Aug 2017, 12:24
JeffTargetTestPrep wrote:
Bunuel wrote:
Train A left Centerville Station, heading toward Dale City Station, at 3: 00 p.m. Train B left Dale City Station, heading toward Centerville Station, at 3: 20 p.m. on the same day. The trains rode on straight tracks that were parallel to each other. If Train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

A. 4: 45 p.m.
B. 5: 00 p.m.
C. 5: 20 p.m.
D. 5: 35 p.m.
E. 6: 00 p.m.


Since 20 minutes = 1/3 hour, we can let the time of Train B = t hours, and thus Train A = t + 1/3 hours.

The distance for Train A is 30(t + 1/3) = 30t + 10, and the distance for train B is 10t; thus:

30t + 10 + 10t = 90

40t = 80

t = 2 hours

So, the trains passed each other at 3:20 + 2 hours = 5:20 p.m.

Answer: C


Jeff - Thanks for answering. May I question as to why you added 2 hours to 3:20 instead of 3:00?
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   21 Aug 2017, 12:46
i have a different suggestion
after 2 hours at 5
train A will be crossing 60 miles and B will be 17.** miles
than after 20 min A will cross 70 mile and B will 20 mile
which is the total length 90 mile
so the ans will be 5.20
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   06 Jun 2020, 09:45
Hi,

I used the same technique but somehow got a difference solution. Adding the 20min in the the time of Train A or subtracting the 20 min from the time of Train B should result in the same solution no?
It obviously doesn't here but I was wondering why as I have done it this way several times and got the right answer for other exercises.

90 = 30(t) 90 = 10 (t-1/3)

30(t) + 10(t) - 10/3 = 90

40t = 90 + 10/3
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink] New post   12 Mar 2024, 11:30
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Re: Train A left Centerville Station, heading toward Dale City Station, at [#permalink]
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