It is currently 23 Oct 2020, 14:19

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Two trains, X and Y, started simultaneously from opposite en

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 13664
Followers: 304

Kudos [?]: 3522 [0], given: 12599

Two trains, X and Y, started simultaneously from opposite en [#permalink]  23 Jun 2020, 04:58
Expert's post
00:00

Question Stats:

72% (02:29) correct 27% (02:52) wrong based on 29 sessions
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5
[Reveal] Spoiler: OA

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.
Eddie Van Halen - Beat it R.I.P.

Founder
Joined: 18 Apr 2015
Posts: 13664
Followers: 304

Kudos [?]: 3522 [0], given: 12599

Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]  23 Jun 2020, 04:58
Expert's post
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!

_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.
Eddie Van Halen - Beat it R.I.P.

GRE Instructor
Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4638 [1] , given: 70

Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]  23 Jun 2020, 05:21
1
KUDOS
Expert's post
Carcass wrote:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Train X completed the 100-mile trip in 5 hours
Speed = distance/time
= 100/5
= 20 mph

Train Y completed the 100-mile trip in 3 hours
Speed = distance/time
= 100/3
33 mph (This approximation is close enough. You'll see why shortly)

How many miles had Train X traveled when it met Train Y?

When the two trains meet, each train will have been traveling for the same amount of time
So, we can write: Train X's travel time = Train Y's travel time

time = distance/speed
We know each train's speed, but not the distance traveled (when they meet). So, let's assign some variables.

Let d = the distance train X travels
So, 100-d = the distance train Y travels (since their COMBINED travel distance must add to 100 miles)

We can now turn our word equation into an algebraic equation.
We get: d/20 = (100 - d)/33
Cross multiply to get: (33)(d) = (20)(100 - d)
Expand: 33d = 2000 - 20d
Add 20d to both sides: 53d = 2000
So, d = 2000/53

IMPORTANT: Before you start performing any long division, first notice that 2000/50 = 40
Since the denominator is greater than 50, we can conclude that 2000/53 is LESS THAN 40
Since only one answer choice is less than 40, the correct answer must be A

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Intern
Joined: 23 Jan 2020
Posts: 18
Followers: 0

Kudos [?]: 18 [2] , given: 9

Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]  27 Jun 2020, 15:28
2
KUDOS
Speed = distance / time

Train X speed is 100/5 = 20 miles per H
Train Y speed is 100/3 = ~33 miles per H

Lets say that the Trains will meet each other after Time T.
Therefore, Dist Traveled by X + Distance Traveled by Y = 100 miles
20T + 33T = 100
T = 100/53 = 1,88

it will take 1,88H for the train to meet.
With train X speed of 20 miles per hour, distance = 20*1,88 = 37.7 =~37.5 (because of using 33 for speed of train Y instead of 100/3)

_________________

still a few Kudos short from my free GRE Prep Club Tests

GRE Instructor
Joined: 10 Apr 2015
Posts: 3871
Followers: 158

Kudos [?]: 4638 [1] , given: 70

Re: Two trains, X and Y, started simultaneously from opposite en [#permalink]  01 Oct 2020, 05:49
1
KUDOS
Expert's post
Carcass wrote:
Two trains, X and Y, started simultaneously from opposite ends of a 100-mile route and traveled toward each other on parallel tracks. Train X, traveling at a constant rate, completed the 100-mile trip in 5 hours; Train Y, traveling at a constant rate, completed the 100-mile trip in 3 hours. How many miles had Train X traveled when it met Train Y?

(A) 37.5
(B) 40.0
(C) 60.0
(D) 62.5
(E) 77.5

Here's another approach....

speed = distance/time
So, Train X's speed = 100/5 = 20 miles per hour
And Train Y's speed = 100/3 ≈ 33 miles per hour

So the shrink rate = 20 + 33 = 53 miles per hour.

At the beginning, the two trains are 100 miles apart.
time = distance/speed
So the time it takes for the trains to meet (i.e., the time it takes for the distance between the two trains to shrink from 100 miles to 0 miles) = 100/53 = a little bit less than 2 hours

How many miles had Train X traveled when it met Train Y?
Distance = (speed)(time)
So Train X's distance traveled = (20)(a little bit less than 2 hours) = a little bit less than 40 miles

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com
If you enjoy my solutions, you'll like my GRE prep course.

Re: Two trains, X and Y, started simultaneously from opposite en   [#permalink] 01 Oct 2020, 05:49
Display posts from previous: Sort by