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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.

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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 01 Dec 2015, 09:42
1
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A
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Difficulty:

  75% (hard)

Question Stats:

65% (02:39) correct 35% (02:56) wrong based on 206 sessions

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Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km

This is not GMAT Material, so only 4 choices.

So I was going through a couple of varied DRT problems, and this one took longer than it should. My question is, how can I approach it differently? Or more efficiently?

So, what I initially tried do was the following

-------|--D----|---R---|---T------|
P--------x-------100---- t-5----
-------|--------|--------|---------|
P--------x-------120---- t+10----
-------|--------|--------|---------|

100t-500 = 120t + 1200

Which is obviously wrong. Then I thought about what I'm actually doing

P's time is five minutes behind T's time after T stops for 10 minutes

P's Time - 5 = Q's Time + 10

P's Time = \(\frac{x}{100}\) and Q's Time = \(\frac{x}{120}\)

So we have:

\(\frac{x}{100}\) = \(\frac{x}{120}\) + \(\frac{15}{60}\)

x=150

So, I suppose I was wondering if anyone has any suggestions on tackling these kind of problems? Or maybe a different approach.

-Thanks
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 01 Dec 2015, 09:55
1
malkadhi wrote:
So I was going through a couple of varied DRT problems, and this one took longer than it should. My question is, how can I approach it differently? Or more efficiently?

Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P.

A) 50 km
B) 100 km
C) 120 km
D) 150 km

This is not GMAT Material, so only 4 choices.

So, what I initially tried do was the following

-------|--D----|---R---|---T------|
P--------x-------100---- t-5----
-------|--------|--------|---------|
P--------x-------120---- t+10----
-------|--------|--------|---------|

100t-500 = 120t + 1200

Which is obviously wrong. Then I thought about what I'm actually doing

P's time is five minutes behind T's time after T stops for 10 minutes

P's Time - 5 = Q's Time + 10

P's Time = \(\frac{x}{100}\) and Q's Time = \(\frac{x}{120}\)

So we have:

\(\frac{x}{100}\) = \(\frac{x}{120}\) + \(\frac{15}{60}\)

x=150

So, I suppose I was wondering if anyone has any suggestions on tackling these kind of problems? Or maybe a different approach.

-Thanks


Make sure to follow posting guidelines (link in my signatures).

All your analyses should either go under "spoilers" or in the next post. This will not dilute the discussion.

We do not usually encourage posting of non GMAT questions as this will only develop bad habits.

But for a one time discussion, your method is absolutely fine. Realize that the for PS questions in GMAT, you must use the options to your advantage. This is not only provide you the correct option but will also help you in spending lesser time than usual. Time management is of utmost importance GMAT.

That being said, once you set up the equation: P's time - 5 min = Q's time + 10 minutes ---> x/100 - 5/60 = x/120 + 10/60 ---> x/100-x/120 = 15/60 . Now use the values given. Only D will satisfy this.
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 02 Dec 2015, 22:00
1
Rich
malkadhi wrote:
Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km


Hi malkadhi,

What is the source of this question (and does the original source have the typos in it or is it just your transcription)? I ask because the prompt only has 4 answer choices and the answers are in KILOMETERS, while the speeds are in MILES per hour. There are plenty of quality GMAT materials that you can use during your studies, so you might want to stop using this resource.

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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 07 Dec 2015, 05:46
2
malkadhi wrote:
Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km



Since every thing is given in the form of time, let us form an equation in time.
Make sure to keep everything in the same units

Assume the distance between A and B to be x miles.

Time taken by Train P = \(\frac{x}{100}\)
Time taken by Train Q = \(\frac{x}{120}\) + 10/60

We are given that Train P reaches 5 minutes after Train Q
Hence \(\frac{x}{100}\) - 5/60 = \(\frac{x}{120}\) + 10/60
\(\frac{x}{100}\) - \(\frac{x}{120}\) = 15/60
\(\frac{6x - 5x}{600}\) = 15/60

x = 150
Option D
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 07 Dec 2015, 08:20
t=time of P
100t=120(t-1/4)
t=3/2 hour
(3/2)(100)=150 miles
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 28 May 2017, 01:40
malkadhi wrote:
Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km

This is not GMAT Material, so only 4 choices.

So I was going through a couple of varied DRT problems, and this one took longer than it should. My question is, how can I approach it differently? Or more efficiently?

So, what I initially tried do was the following

-------|--D----|---R---|---T------|
P--------x-------100---- t-5----
-------|--------|--------|---------|
P--------x-------120---- t+10----
-------|--------|--------|---------|

100t-500 = 120t + 1200

Which is obviously wrong. Then I thought about what I'm actually doing

P's time is five minutes behind T's time after T stops for 10 minutes

P's Time - 5 = Q's Time + 10

P's Time = \(\frac{x}{100}\) and Q's Time = \(\frac{x}{120}\)

So we have:

\(\frac{x}{100}\) = \(\frac{x}{120}\) + \(\frac{15}{60}\)

x=150

So, I suppose I was wondering if anyone has any suggestions on tackling these kind of problems? Or maybe a different approach.

-Thanks


Quick way of doing this is by using ratios.
Let the number of minutes that it takes P = t minutes.

So, for Q it is = t - 15 minutes.

Ratio of their speeds = 5:6
So, ratio of their times = 6:5
\(\frac{5}{6} = \frac{(t-15)}{t}\)

t = 90 minutes..or 1.5 hrs..

Thus, distance is
\(1.5*100 = 150 km\)

(D)
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 28 May 2017, 01:45
Answer would be 150 Km ..Using options we can reach the answer . P will travel for 15 more mins than Q


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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 28 May 2017, 07:28
If Q had not stopped for 10 minutes, it would have reached Station B 15 minutes earlier than P. That is, when Q reaches B, P is still 100/4=25 miles behind. Which means that in the time that Q covers the distance AB (lets assume this to be d miles) P covers (d-25)miles. Since the ratios of the speeds of the two trains is equal to ratio of the distances covered by them in the same time, we can write:
120/100=d/(d-25)
Thus, d=150. Answer: D
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 28 Jul 2017, 13:49
For Train P
S = 100mph
D = x miles
T = t hrs

For Train Q.
S= 120mph
D = xmiles
T = t- 1/6 -1/12 (Since Train Q stopped for 10 min, i.e. 1/6hrs and reached 5 min earlier, i.e, 1/12 hrs; Therefore total time the Train Q took was t - 1/6-1/12)

Distance = Speed * Time
100t = 120 *(t-1/6-1/12)
100t = 120t -20-10
20t =30
t= 1.5 hrs

Distance = X miles = 100*t = 150 miles


malkadhi wrote:
Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km

This is not GMAT Material, so only 4 choices.

So I was going through a couple of varied DRT problems, and this one took longer than it should. My question is, how can I approach it differently? Or more efficiently?

So, what I initially tried do was the following

-------|--D----|---R---|---T------|
P--------x-------100---- t-5----
-------|--------|--------|---------|
P--------x-------120---- t+10----
-------|--------|--------|---------|

100t-500 = 120t + 1200

Which is obviously wrong. Then I thought about what I'm actually doing

P's time is five minutes behind T's time after T stops for 10 minutes

P's Time - 5 = Q's Time + 10

P's Time = \(\frac{x}{100}\) and Q's Time = \(\frac{x}{120}\)

So we have:

\(\frac{x}{100}\) = \(\frac{x}{120}\) + \(\frac{15}{60}\)

x=150

So, I suppose I was wondering if anyone has any suggestions on tackling these kind of problems? Or maybe a different approach.

-Thanks
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 06 Aug 2017, 03:40
Total time taken by Q =\(\frac{D}{120} + \frac{10}{60}\)
Total time taken by P =\(\frac{D}{100}\) = Total time take by Q + \(\frac{5}{60}\)
\(\frac{D}{120} + \frac{10}{60}\) + \(\frac{1}{12}\) = \(\frac{D}{100}\)

\(\frac{D+30}{120} = \frac{D}{100}\)

Solving for D --> D = 150
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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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New post 06 Aug 2017, 21:05
malkadhi wrote:
Train P and Q travel from A to B at 100 mph, and 120 mph respectively. Train Q stops for 10 minutes at station C, but reaches Station B, 5 Minutes before Train P. what is the distance between A and B.

A) 50 km
B) 100 km
C) 120 km
D) 150 km


Let the distance from \(A\) to \(B = D\)

Let the time for Train \(P\) to travel from \(A\) to \(B = t\)

Speed of train \(P = 100\) mph

Distance , \(D = 100*t\) --------- (i)

Time for Train \(Q\) to travel from \(A\) to \(B = t - (10+5) = t - 15\)

Speed of train \(Q = 120\) mph

Distance , \(D = 120 (t-15)\) ---------- (ii)

Distance is same for both trains. Therefore equating (i) and (ii) we get;

\(100*t = 120(t-15)\)

\(100t = 120t - 1800\)

\(20t = 1800\)

\(t = 90\) mins or \(1.5\) hours

Substituting value of '\(t\)' in distance formula, we get;

\(D = 100t = 100 * 1.5\) hours \(= 150\) km

Answer (D)...


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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively. &nbs [#permalink] 14 Sep 2018, 21:34
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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.

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