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# If two trains are 120 miles apart and are traveling toward each other

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Joined: 28 Sep 2016
Posts: 1
If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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Updated on: 01 Oct 2016, 02:20
10
00:00

Difficulty:

55% (hard)

Question Stats:

64% (01:54) correct 36% (01:55) wrong based on 221 sessions

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If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

As the question ask how far apart they will be 1 hour before they meet, I first calculated when they meet : 120- (30+40)= 12/7 h
so one hour before they meet is 12/7 - 1 = 5/7 h.
when the time is 5/7 they are 5/7 *70= 50 miles far apart .
anyway, the Question bank says that the correct answer is E, 70.
Can anyone tell me why? I think 70 is how much they are far apart 1 hour after they leave, not 1 hour before they meet.

Originally posted by mc563427 on 01 Oct 2016, 02:12.
Last edited by Bunuel on 01 Oct 2016, 02:20, edited 1 time in total.
Renamed the topic and edited the question.
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Math Expert
Joined: 02 Sep 2009
Posts: 52108
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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01 Oct 2016, 02:23
5
mc563427 wrote:
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

As the question ask how far apart they will be 1 hour before they meet, I first calculated when they meet : 120- (30+40)= 12/7 h
so one hour before they meet is 12/7 - 1 = 5/7 h.
when the time is 5/7 they are 5/7 *70= 50 miles far apart .
anyway, the Question bank says that the correct answer is E, 70.
Can anyone tell me why? I think 70 is how much they are far apart 1 hour after they leave, not 1 hour before they meet.

The combined rate of the two trains is 30 + 40 = 70 miles per hour. Therefore 1 hour before they meet the must be 70 miles apart (in the final 1 hour they will cover 70 miles to meet).

Answer: E.

P.S. Please follow the rules when posting a question: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Joined: 02 Sep 2009
Posts: 52108
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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01 Oct 2016, 02:24
1
Bunuel wrote:
mc563427 wrote:
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

As the question ask how far apart they will be 1 hour before they meet, I first calculated when they meet : 120- (30+40)= 12/7 h
so one hour before they meet is 12/7 - 1 = 5/7 h.
when the time is 5/7 they are 5/7 *70= 50 miles far apart .
anyway, the Question bank says that the correct answer is E, 70.
Can anyone tell me why? I think 70 is how much they are far apart 1 hour after they leave, not 1 hour before they meet.

The combined rate of the two trains is 30 + 40 = 70 miles per hour. Therefore 1 hour before they meet the must be 70 miles apart (in the final 1 hour they will cover 70 miles to meet).

Answer: E.

P.S. Please follow the rules when posting a question: rules-for-posting-please-read-this-before-posting-133935.html Thank you.

Similar question to practice: 12-easy-pieces-or-not-126366.html#p1033924

Hope it helps.
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Intern
Joined: 07 Mar 2013
Posts: 5
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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17 Oct 2016, 05:30
1
this is a little lengthier way of doing but mistake proof method.
They would meet in 120/70 = 12/7 hours
1 hour earlier 5/7 hours
distance between trains = total distance -(distance covered by train A + distance covered by train B)

= 120-(5/7(40+30)) [ distance of A = 5/7* 40; like wise distance by B]
= 70 Km

Kudos! if u like this
SVP
Joined: 12 Dec 2016
Posts: 1610
Location: United States
GMAT 1: 700 Q49 V33
GPA: 3.64
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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03 Apr 2017, 18:31
It is still hard for me to focus on the right detail. It is because in this case, I may miss one or two important details in quantitative problems.
Target Test Prep Representative
Status: Head GMAT Instructor
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Posts: 2830
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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06 Apr 2017, 08:43
1
mc563427 wrote:
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

Since we have a converging rate problem, we can use the following formula:

distance 1 train + distance 2 train = total distance

We can let t be the time the two trains will meet. Thus:

30t + 40t = 120

70t = 120

t = 120/70 = 12/7 hours

Since we want to find the distance apart 1 hour before they meet, the distance traveled by one train is 30(12/7 - 1) = 30(5/7) = 150/7 miles and the distance traveled by the other train is 40(12/7 - 1) = 40(5/7) = 200/7 miles. Thus, the total distance traveled by the two trains is 150/7 + 200/7 = 350/7 = 50 miles. Therefore, they are 120 - 50 = 70 miles apart 1 hour before they meet.

Alternative solution:

A much shorter approach to solve this problem is to argue the following:

Since in 1 hour, train 1 travels 30 miles and train 2 travels 40 miles, 1 hour before they meet, they should be 30 + 40 = 70 miles apart.

Answer: E
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Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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08 Apr 2017, 06:00
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

relative speed is 30+40=70 miles per hour

answer is E
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Joined: 14 Dec 2017
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Location: India
Re: If two trains are 120 miles apart and are traveling toward each other  [#permalink]

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14 Jun 2018, 13:19
mc563427 wrote:
If two trains are 120 miles apart and are traveling toward each other at constant rate of 30 miles per hour and 40 miles per hour, respectively, how far apart will they be 1 hour before they meet?

(A) 10
(B) 30
(C) 40
(D) 50
(E) 70

Relative speed of the two trains = 30 + 40 = 70 miles per hour

In the last 1 hour before they meet, the trains together have to travel for 1 hour at a speed of 70 miles per hour.

Hence they will be 70 miles apart,1 hour before they meet.

Answer E.

Thanks,
GyM
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Re: If two trains are 120 miles apart and are traveling toward each other &nbs [#permalink] 14 Jun 2018, 13:19
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# If two trains are 120 miles apart and are traveling toward each other

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