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Math Expert V
Joined: 02 Sep 2009
Posts: 58445
Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 75% (02:27) correct 25% (02:39) wrong based on 394 sessions

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Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80

Kudos for a correct solution.

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Intern  Joined: 13 Jan 2015
Posts: 13
GMAT 1: 750 Q50 V41 GPA: 3.86
Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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The easiest way to think about this problem is to start off conceptually.

If the total distance between the trains after 2/3 hours (40 minutes) is 100 miles, then the combined speed of the trains must be 150 mph. (using RTD tables, 100 * 3/2 = 150)
Therefore, if train x is going 30 mph faster than train y, then train x's speed must be -> x + (x-30) = 150 -> x = 90

Therefore, after 40 minutes, traveling at 90 mph, train x has traveled 60 miles (90 * 2/3 hours = 60 miles).

Originally posted by robertsonsd on 27 Mar 2015, 08:02.
Last edited by robertsonsd on 26 Feb 2016, 21:51, edited 1 time in total.
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Intern  Joined: 17 Feb 2015
Posts: 27
GPA: 3
Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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Let's say train X runs at z miles/hour, then train Y will be running at (z-30) miles/hour
Since they are 100 miles apart after 40 minutes = 40/60 hours = 2/3 hours

$$z*\frac{2}{3} + (z-30)*\frac{2}{3} = 100$$
$$2*z*\frac{2}{3} -20 = 100$$
$$z*\frac{2}{3} = 60$$ = distance travelled by train X in 40 minutes.
Director  Joined: 07 Aug 2011
Posts: 502
Concentration: International Business, Technology
GMAT 1: 630 Q49 V27 Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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Bunuel wrote:
Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80

Kudos for a correct solution.

x=Speed of Train X
y= X-30
relative speed = 2X-30
T= 2/3 hr

(2X-30) *2/3= 100
X=90 mph

distance travelled = 90*2/3 = 60

Manager  S
Joined: 24 Jan 2015
Posts: 68
GPA: 4
WE: Consulting (Pharmaceuticals and Biotech)
Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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3
2
Let the rate of the Train Y be R
Then the rate of the Train X will be R+30 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+30) [add the rates] i.e. 2R+30

d=100 and t = 40 min i.e 40/60 hr

using RTD table, (2R+30) * 40/60 = 100 ==> R= 60 miles/hr

So the rate of train X is 90 miles/hr (since R+30)

The distance traveled by Train X in 40 min is R*T = 90 * 40?/60 = 60 miles (C)
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Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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Its a relative speed problem.

Relative speed of train X with reference to train Y = 100*60/40 = 150

Since train X and Y are going in opposite direction, the relative speed would be sum of individual speeds.
Hence,

x -30 + x = 150 => x=90.

Speed of train X is 90 and hence distance traveled in 40 minutes would be 90*40/60 = 60 miles.

C is the correct answer.
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Intern  Joined: 04 Mar 2015
Posts: 4
Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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2

if they travel 100 miles in 40 mins
=> in 1 hr they will travel (100/40)*60 = 150 miles
assume speed of train X = y+30
and seepd of 2nd train = y
now since the trains are moving in different directions the speed of both the trains add up
=> y + 30 + y = 150 (because in one 1 hr they travel 150 miles)
=> 2y + 30 = 150
=> y = 60
=> speed of train x = 90
hence in 40 mins it will travel 60 miles ( 90 *40/60)
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Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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let's say speed of y be a km/h and speed of x is (a+30)km/h
since they are traveling in opposite directions, we need to add their speed,
therefore total speed is a+a+30 =(2a+30)km/h
in 2/3 = 0.66 hours they traveled 100 km, so distance/time = speed
100/0.66=2a+30
a=60km/h
so speed of x is 60+30 = 90km/h
and x will cover 90*(2/3) = 60km
Director  G
Joined: 23 Jan 2013
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Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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(2/3)x + (2/3)*(x+30)=100

(4/3)*x=80

x=60

60+30=90*(2/3)=60

C
Retired Moderator P
Status: The best is yet to come.....
Joined: 10 Mar 2013
Posts: 484
Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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For relative speed of bodies moving in opposite direction, the equation is (Sx + Sy) X t = Distance

Here, total distance need to be covered is 100 miles

Let the speed of train Y is y. Therefore, the speed of train X would be y+30.

So, the equation becomes $$(y+3+y)t=100=>y=60$$

So, the speed of train X is 60+30=90

In 60 minutes train x travels 90 miles. So in 40 minutes it will travel 60 miles.
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Hasan Mahmud
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Re: Train X and train Y pass one another traveling in opposite directions.  [#permalink]

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from given info
speed of train X; x
speed of train Y ; y
given ; speed of train X ; y+30
so ;
(2y+30)*40/60 = 100
y = 60 mph
x= 90mph
distance of X will be 90*40/60 ; 60 miles
IMO C

Bunuel wrote:
Train X and train Y pass one another traveling in opposite directions. Forty minutes later they are 100 miles apart. If train X’s constant speed is 30 miles per hour greater than train Y’s, how far does train X travel during that time?

A. 28
B. 40
C. 60
D. 72
E. 80

Kudos for a correct solution. Re: Train X and train Y pass one another traveling in opposite directions.   [#permalink] 01 Oct 2019, 18:26
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