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• ### Essential GMAT Time-Management Hacks

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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 15 Sep 2015 Posts: 8 Train P and Q travel from A to B at 100 mph, and 120 mph respectively. [#permalink] ### Show Tags 01 Dec 2015, 09:42 1 5 00:00 Difficulty: 75% (hard) Question Stats: 65% (02:39) correct 35% (02:56) wrong based on 206 sessions ### HideShow timer Statistics 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 Joined: 20 Mar 2014 Posts: 2635 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] ### Show Tags 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. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12841 Location: United States (CA) 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] ### Show Tags 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. GMAT assassins aren't born, they're made, _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Posts: 389
Location: India
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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

07 Dec 2015, 05:46
2
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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Posts: 1108
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

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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GPA: 3
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

28 May 2017, 01:40
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

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]

### Show Tags

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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Joined: 09 Nov 2015
Posts: 32
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

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)
Intern
Joined: 20 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]

### Show Tags

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

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
Manager
Joined: 23 Jul 2015
Posts: 157
Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

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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Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
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Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

### Show Tags

06 Aug 2017, 21:05
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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Re: Train P and Q travel from A to B at 100 mph, and 120 mph respectively.  [#permalink]

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14 Sep 2018, 21:34
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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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