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
Hi, I found the situation of this question is not very clear.. I want to know how we can approach this, please.![]()
15 minutes
25 minutes
1 hour 15 minutes
1 hour 40 minutes
4 hours 30 minutes
OE
[Reveal] Spoiler:
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.
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.