A woman is planning a trip that involves 3 connecting trains

This is a reworded OG question: an-airline-passenger-is-planning-a-trip-that-involves-three-108830.html

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.

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.

Answer: B

Depart from X at 8 am

Arrive at Y at 9:45 am

Wait 15 minutes****


Depart Y at 10 am

Arrive at Z at 12:20 pm

Wait 10 minutes****

Depart from Z at 12:30 pm


Total Minimum Wait Time = 15 + 10 = 25 minutes

-B-


I always find it quickest on these types of scheduling problems to follow a train all the way through from the 1st time from the 1st station, trying to minimize along the way.

Usually within 3 to 4 departures I can see a pattern in which the minimum time can no be lowered any further (or at least can eliminate 3 answers)

Some ppl prefer writing out all the schedules. It takes too long for me.

Posted from my mobile device

woww!
very beautifully explained
I struggled for 20 mins before looking into this solution.
Now, my mind is clear

Given: 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.

Asked: 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.?

Station X - Departure	Station Y - Arrival	Station Y - Departure	Station Y - Waiting time	Station Z - Arrival	Station Z - Departure	Station Z - Waiting Time	Total Waiting Time
6 am	7:45	9 am	1:15 hrs	-	8 am	-	-
7 am	8:45	9 am	0:15 hrs	11:20 am	11:45 am	0:25 hrs	0:40 hrs
8 am	9:45	10 am	0:15 hrs	12:20 am	12:30 am	0:10 hrs	0:25 hrs

Minimum waiting time = 15 + 10 = 25 minutes

IMO B

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