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# A woman is planning a trip that involves 3 connecting trains

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Senior Manager
Joined: 21 Oct 2013
Posts: 419
A woman is planning a trip that involves 3 connecting trains  [#permalink]

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13 Jan 2014, 12:07
4
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Difficulty:

85% (hard)

Question Stats:

62% (03:31) correct 38% (03:08) wrong based on 224 sessions

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A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes

OE
Trains coming from X arrive at Y at 45 minutes past the hour.
Trains leave Y on the hour and the half-hour. So minimum wait at Y will be 0:15.
This could be 8:45 − 9:00 am, 9:45 − 10:00 am, 10:45 − 11:00 am, etc.

Trains from Y will reach Z at 20 and 50 minutes past the hour, with the first arriving at 11:20.

Trains leave Z at various times, creating waits as short as 10 minutes (12:20-12:30) and as long as 40 minutes (11:50-12:30).

For shortest total waiting time possible, need to combine a 15-minute wait for the second train with a 10-minute wait for third train.

This will happen if the woman takes the 8:00 train from X, the 10:00 train from Y, and the 12:30 train from Z.

Hi, I found the situation of this question is not very clear.. I want to know how we can approach this, please.
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Re: A woman is planning a trip that involves 3 connecting trains  [#permalink]

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02 Mar 2015, 01:28
7
1
goodyear2013 wrote:
A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes

OE
Trains coming from X arrive at Y at 45 minutes past the hour.
Trains leave Y on the hour and the half-hour. So minimum wait at Y will be 0:15.
This could be 8:45 − 9:00 am, 9:45 − 10:00 am, 10:45 − 11:00 am, etc.

Trains from Y will reach Z at 20 and 50 minutes past the hour, with the first arriving at 11:20.

Trains leave Z at various times, creating waits as short as 10 minutes (12:20-12:30) and as long as 40 minutes (11:50-12:30).

For shortest total waiting time possible, need to combine a 15-minute wait for the second train with a 10-minute wait for third train.

This will happen if the woman takes the 8:00 train from X, the 10:00 train from Y, and the 12:30 train from Z.

Hi, I found the situation of this question is not very clear.. I want to know how we can approach this, please.

Make a departure arrival diagram to minimize the waiting time.
Attachment:

FullSizeRender.jpg [ 1.49 MiB | Viewed 3341 times ]

Trains depart from X at 6/7/8/9 and reach Y at 7:45/8:45/9:45 etc
Trains depart from Y at 9/9:30/10/10:30 etc. This means a minimum wait of 15 mins is required at Y.
They arrive at Z at 11:20/11:50/12:20/12:50. They depart from Z at 8/8:45/9:30/10:15/11/11:45/12:30 and so on. Note that if she arrives at Z at 20 mins past the hour, she will need to wait for at least 10 mins for 12:30/3:30 etc train. If she arrives at 50 mins past the hour, again she needs to wait for at least 10 mins to take the 2 o clock train. So anyway 10 mins at Z is a given.

So minimum she will need to wait for 15+10 = 25 mins.
This works out if she takes 8 o clock train from X, reaches Y at 9:45, takes 10 o clock train from Y and reaches Z at 12:20 and takes 12:30 train from Z.

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Karishma
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Re: A woman is planning a trip that involves 3 connecting trains  [#permalink]

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13 Jan 2014, 12:15
goodyear2013 wrote:
A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes

OE
Trains coming from X arrive at Y at 45 minutes past the hour.
Trains leave Y on the hour and the half-hour. So minimum wait at Y will be 0:15.
This could be 8:45 − 9:00 am, 9:45 − 10:00 am, 10:45 − 11:00 am, etc.

Trains from Y will reach Z at 20 and 50 minutes past the hour, with the first arriving at 11:20.

Trains leave Z at various times, creating waits as short as 10 minutes (12:20-12:30) and as long as 40 minutes (11:50-12:30).

For shortest total waiting time possible, need to combine a 15-minute wait for the second train with a 10-minute wait for third train.

This will happen if the woman takes the 8:00 train from X, the 10:00 train from Y, and the 12:30 train from Z.

Hi, I found the situation of this question is not very clear.. I want to know how we can approach this, please.

This is a reworded OG question: an-airline-passenger-is-planning-a-trip-that-involves-three-108830.html
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Concentration: Finance, General Management
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A woman is planning a trip that involves 3 connecting trains  [#permalink]

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19 Jun 2015, 06:16
1
I would prefer back solving for this question.

Reached Z @ 3:30 PM, from Y-->Z it will take 140 minutes, so she should have started from Y @ 1:10 PM but trains from Y to Z leaves at every 30mins starting at 9am,therefore she should board into the train @1PM and wait at station Z for 10minutes for her next train from station Z.

Now, X --> Y journey:

To reach Y at 1PM she should start from X by 11AM atleast as, journey time is 105minutes .If she will start from station X by 11AM then she will reach Y by 12:45 PM, hence will wait for 15minutes before she board into 1PM train from station Y.

Total waiting time= 15+10=25 minutes.

Cheers,
Gaurav
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Posts: 2600
Location: United States (IL)
Concentration: Finance, Economics
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Re: A woman is planning a trip that involves 3 connecting trains  [#permalink]

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13 Jan 2016, 18:36
kind of tricky one...but as bunuel said..looks like an og question...
if passenger leaves at 8AM, then arrives at Y at 9:45AM, departs at 10AM, or waits 15 minutes (always 15 mins, since the timing is always 15 mins either behind or late)

trains at Z depart at 8:45, 9:30, 10:15, 11:00, 11:45, 12:30, 1:15PM, 2PM, 2:45PM
8:45, 9:30, 10:15, and 11:00 can't be, so right away out. note that the train from Y to Z alone takes 2h20min, and train Y starts at 9AM.
if starts at 9AM, then it will arrive at Z at 11:20, which makes 25 mins wait time at Z.
if starts at 9:30 -> arrives at 11:50 - wait time - 40 minutes. nope
if starts at 10 -> arrives at 12:20 - wait time 10 minutes.
if starts at 10:30 -> arrives at 12:50 -> wait time 25 minutes
if starts at 11 -> arrives at 1:20PM, wait time 40 minutes.
if starts at 11:30 -> arrives at 1:50 -> wait time 10 minutes.
if starts at 12 -> arrives at 12:20 -> wait time 25 mins.
thus, the min time to wait would be 10 mins at Z.
15+10 = 25
can't be 15, since the time to wait at Y only is 15, and there is no such way that there is no wait time at Z.
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Re: A woman is planning a trip that involves 3 connecting trains  [#permalink]

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19 Apr 2018, 15:58
goodyear2013 wrote:
A woman is planning a trip that involves 3 connecting trains that depart from Stations X, Y, and Z, respectively. The first train leaves Station X every hour, beginning at 6 a.m., and arrives at Station Y 1(3/4) hours later. The second train leaves Station Y every half hour, beginning at 9 a.m., and arrives at Station Z 2(1/3) hours later. The third train leaves Station Z every 45 minutes, beginning at 8 a.m. What is the least total amount of time the woman must spend waiting between trains if all trains depart and arrive on schedule, and if she arrives at Station Z no later than 3:30 p.m.?
15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes

We see that the total wait time is the total time waiting at stations Y and Z assuming that she doesn’t have to wait at station X. Let’s also let the trains leaving at stations X, Y and Z be trains X, Y and Z, respectively.

Assuming she arrives at station X exactly on the hour, except for arriving at 6 am at station X, she must wait 15 minutes at station Y for train Y. For example, if she catches train X at station X at 7 am, she will arrive at station Y at 8:45 am and catch train Y at 9 am. If she catches train X at station X at 8 am, she will arrive at station Y at 9:45 am and catch train Y at 10 am.

We see that the minimum wait time at station Y is 15 minutes. Now let’s see how we can minimize the wait time at station Z. Since train Z leaves station Z every 45 minutes beginning at 8 am, train Z leaves station Z at 8 am, 8:45 am, 9:30 am, 10:15 am, 11 am, 11:45 am, 12:30 pm, etc. Also, since train Y takes 2 hours and 20 minutes to arrive at station Z and it leaves station Y every 30 minutes beginning at 9 am, train Y will arrive at station Z at 11:20 am, 11:50 am, 12:20 pm, etc. We see that the minimum wait time is 10 minutes if she can arrive at station Z at 12:20 pm and take train Z at 12:30 pm.

Thus the minimum total wait time is 15 + 10 = 25 minutes.

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Re: A woman is planning a trip that involves 3 connecting trains &nbs [#permalink] 19 Apr 2018, 15:58
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