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# 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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01 Dec 2015, 10:42
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Question Stats:

59% (02:01) correct 41% (02:14) wrong based on 190 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

[Reveal] Spoiler:
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
[Reveal] Spoiler: OA
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Joined: 20 Mar 2014
Posts: 2689
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
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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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01 Dec 2015, 10:55
1
KUDOS
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

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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02 Dec 2015, 23:00
1
KUDOS
Expert's post
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.

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Senior Manager
Joined: 20 Aug 2015
Posts: 394
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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07 Dec 2015, 06:46
1
KUDOS
Expert's post
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
Director
Joined: 07 Dec 2014
Posts: 929
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively. [#permalink]

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07 Dec 2015, 09:20
t=time of P
100t=120(t-1/4)
t=3/2 hour
(3/2)(100)=150 miles
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Posts: 291
Location: India
Concentration: Marketing, Finance
Schools: Simon '20
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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28 May 2017, 02:40
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

[Reveal] Spoiler:
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 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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28 May 2017, 02:45
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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Luckisnoexcuse

Intern
Joined: 09 Nov 2015
Posts: 26
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively. [#permalink]

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28 May 2017, 08:28
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)
Intern
Joined: 21 Mar 2012
Posts: 19
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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28 Jul 2017, 14:49
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

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

[Reveal] Spoiler:
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
Manager
Joined: 23 Jul 2015
Posts: 166
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively. [#permalink]

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06 Aug 2017, 04:40
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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06 Aug 2017, 22:05
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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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.   [#permalink] 06 Aug 2017, 22:05
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