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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Train P and Q travel from A to B at 100 mph, and 120 mph respectively.

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Intern  Joined: 15 Sep 2015
Posts: 8
Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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8 00:00

Difficulty:   65% (hard)

Question Stats: 66% (02:44) correct 34% (02:52) wrong based on 264 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
CEO  S
Joined: 20 Mar 2014
Posts: 2596
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44 GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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1
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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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Rich
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

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.

GMAT assassins aren't born, they're made,
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Senior Manager  Joined: 20 Aug 2015
Posts: 386
Location: India
GMAT 1: 760 Q50 V44 Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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3
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
VP  P
Joined: 07 Dec 2014
Posts: 1224
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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t=time of P
100t=120(t-1/4)
t=3/2 hour
(3/2)(100)=150 miles
Senior Manager  G
Joined: 03 Apr 2013
Posts: 264
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41 GPA: 3
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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1
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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GMAT 1: 630 Q47 V29 GMAT 2: 740 Q51 V38 Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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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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Luckisnoexcuse
Manager  S
Joined: 09 Nov 2015
Posts: 135
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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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
Intern  B
Joined: 21 Mar 2012
Posts: 23
Location: India
GMAT 1: 710 Q49 V38 Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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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

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
Current Student S
Joined: 23 Jul 2015
Posts: 143
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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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
Director  V
Joined: 04 Dec 2015
Posts: 743
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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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

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

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Schools: XLRI"20
GMAT 1: 700 Q50 V34 GPA: 3.5
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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How do we know both the trains started at same time? This question requires some assumptions Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.   [#permalink] 01 Jan 2019, 20:33
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