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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Train A and B, 455 miles apart, are traveling toward each ot

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Director  Joined: 29 Nov 2012
Posts: 685
Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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10 00:00

Difficulty:   55% (hard)

Question Stats: 70% (02:41) correct 30% (03:01) wrong based on 246 sessions

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Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

Any faster approaches?

train A travels for an hour and 45 mins so 7/4. distance travelled = 7/4 * 60 = 105.

since they track is 455 miles and Train A has travelled 105 miles. Now 350 miles left.

Since when they meet distance would be equal so 60t + 45t = 350

t = 10/3 so its 3 hours and 20 mins + 5 : 45 = 9:05 pm
Math Expert V
Joined: 02 Sep 2009
Posts: 58991
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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fozzzy wrote:
Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

Any faster approaches?

train A travels for an hour and 45 mins so 7/4. distance travelled = 7/4 * 60 = 105.

since they track is 455 miles and Train A has travelled 105 miles. Now 350 miles left.

Since when they meet distance would be equal so 60t + 45t = 350

t = 10/3 so its 3 hours and 20 mins + 5 : 45 = 9:05 pm

It's pretty much it.

In 1 hour and 45 minutes (7/4 hours) A traveled 7/4*60 = 105 miles.

Distance to cover 455 - 105 = 350 miles.

Combined rate (60 + 45) = 105 miles per hour, which mean that they will cover 350 miles in 350/105 = 10/3 hours (3 hours and 20 minutes).

5:45 pm + 3 hours and 20 minutes = 9:05 pm.

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Intern  Joined: 05 Oct 2013
Posts: 20
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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We have: 455 = 60*1.75 + x*105. So we get x = (455-105)/105= 10/3 = 3h 20mins.
So the the answer should be 5:45 + 3:20=9:05 (C)
SVP  Joined: 06 Sep 2013
Posts: 1553
Concentration: Finance
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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fozzzy wrote:
Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

Any faster approaches?

train A travels for an hour and 45 mins so 7/4. distance travelled = 7/4 * 60 = 105.

since they track is 455 miles and Train A has travelled 105 miles. Now 350 miles left.

Since when they meet distance would be equal so 60t + 45t = 350

t = 10/3 so its 3 hours and 20 mins + 5 : 45 = 9:05 pm

Nice problem, here we go

First, since A has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles

Then remaining distance to be traveled will be 455 - 105 = 350 miles

Now, using relative rates (105)(t) = 350

This gives 10/3 hours

Now 5.45pm + 10/3 hours gives us 9.05pm

Hope it helps!
Cheers!
J Intern  Joined: 13 Dec 2013
Posts: 5
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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Why is this different from the way that you are solving it?

D1= D2 then 60T = 45( T + 1.45h)

Once we know the time we could add it up to the starting time to know when is the meeting time i think.

Thank you very much in advance,
Math Expert V
Joined: 02 Sep 2009
Posts: 58991
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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guimooow wrote:
Why is this different from the way that you are solving it?

D1= D2 then 60T = 45( T + 1.45h)

Once we know the time we could add it up to the starting time to know when is the meeting time i think.

Thank you very much in advance,

What is T in your equation? Which distances are you equating?

If you want to solve for T it should be: 60T + 45(T-7/4) = 455, where T is the total time for A. Though it's much better to solve with step by step approach explained here: train-a-and-b-455-miles-apart-are-traveling-toward-each-ot-161174.html#p1275213
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Posts: 2497
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30 GPA: 3.92
WE: General Management (Transportation)
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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fozzzy wrote:
Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

i tried to visualize it...
so train A leaves at 4PM. at 5, 60 of the distance would be covered. distance between trains = 395.
in another 45 mins, the train would travel another 45 miles. distance between them = 350.
train B starts...now the distance between them would shrink by 60+45 or 105 miles per hour.
350/105 = 10/3.
so additional 3 hours and 20 minutes after train B starts:
9:05PM
Intern  B
Joined: 13 Dec 2018
Posts: 45
Location: India
GPA: 3.94
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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In 1 hour and 45 minutes A will travel 7/4*60 = 105 miles.
Remaining Distance to cover 455 - 105 = 350 miles.
Combined speed of both the trains (60 + 45) = 105 mph
They will cover 350 miles in 350/105 = 10/3 hours (3 hours and 20 minutes).
So, 5:45 + 3 hours and 20 minutes = 9:05 pm.
Hence, C.
GMAT Club Legend  D
Joined: 18 Aug 2017
Posts: 5260
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: Train A and B, 455 miles apart, are traveling toward each ot  [#permalink]

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given distance 455 miles
so at 4pm to 5:45 PM ; we have 1 hr 45 mins ; 105mins
distance covered by A ; 60*105/60 ; 105 miles
so both A &B start common at 350 miles
relative speed ; 60+45 ; 105 mph
time when they meet ; 350/105 ; 3.33hrs or say 3 hrs +.33*60 ; 3 hrs 20 mins from 5:45 PM
i.e 9:05 PM
IMO C

fozzzy wrote:
Train A and B, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train A left at 4 pm traveling at a speed of 60 miles per hour, and train B left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?

A. 7:20 pm
B. 8:55 pm
C. 9:05 pm
D. 9:20 pm
E. 9:25 pm

Any faster approaches?

train A travels for an hour and 45 mins so 7/4. distance travelled = 7/4 * 60 = 105.

since they track is 455 miles and Train A has travelled 105 miles. Now 350 miles left.

Since when they meet distance would be equal so 60t + 45t = 350

t = 10/3 so its 3 hours and 20 mins + 5 : 45 = 9:05 pm Re: Train A and B, 455 miles apart, are traveling toward each ot   [#permalink] 02 Oct 2019, 18:50
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