Question

Information: All trains need to run to a timetable so that passengers may find the train they want to use easily and conveniently. When the line is opened a timetable must be produced. The government have stated that they require three trains per hour to run between London and Birmingham and also three per hour to run between Birmingham and London. The government have stated that: the journey time will be 49 minutes, it takes 6 minutes to empty the train, it takes 12 min utes to clean and prepare the train, it takes 19 minutes to perform ticket checks and let passengers board the train. Train services start at 07:01 in London and finish at about 22:00. Train services start at 07:00 in Birmingham and finish at about 22:00. a) Question: Using this information, create a train timetable for a single day for Birmingham station and another for London station. Your timetable will show the times each train departs and arrives as well as the times the train is emptied, cleaned, ready to be boarded, etc. Each train that arrives or departs must be shown and care must be taken to show that your timetable actually works, ideally by labelling each train with a number. We recommend that you write out any supporting mathematics by hand.

Answer 1

Time Train NO. LB601 LB101 LB201 LB301 LB401 LB501 LB701 LB801 LB102 00:06 emptying 00:12 Cleaning 00:19 Boarding 08:35 07:55 08:15 08:55 09:22 09:34 08:07 08:27 08:47 09:07 08:46 08:26 09:06 09:26 09:53 00:20 London 07:01 07:21 97:41 08:01 08:26 08:46 09:06 09:26 09:53 00:49 Birmingham 07:50 08:10 08:30 08:50 09:15 09:35 09:55 10:15 10:42 BL501 BL601 BL701 BL801 BL101 BL201 BL301 BL401 BL502 00:06 emptying 7:56 8:16 8:36 8:56 9:21 00:12 Cleaning 00:19 Boarding 9:33 8:08 8:28 8:48 9:08 8:27 8:47 9:07 9:27 9:52 00:20 Birmingham 07:20 07:40 08:27 07:00 08:00 08:47 09:07 09:27 09:47 00:49 London 9:36 07:49 08:09 08:29 08:49 9:16 9:56 10:16 10:36

Time Train NO LB502 LB602 LB702 LB802 LB202 LB302 LB402 LB103 LB203 00:06 emptying 00:12 Cleaning 00:19 Boarding 09:42 10:22 10:42 11:02 11:22 11:42 12:22 10:02 12:02 09:54 10:14 10:34 10:54 11:14 11:34 11:54 12:14 12:34 10:13 10:33 10:53 12:33 11:13 11:33 11:53 12:13 12:53 10:13 10:33 11:13 11:33 11:53 12:13 12:33 12:53 00:20 London 10:53 00:49 Birmingham 11:02 11:22 11:42 12:02 12:22 12:42 13:02 13:22 13:42 BL602 BL702 BL802 BL102 BL202 BL302 BL402 BL503 BL603 00:06 emptying 9:41 10:01 10:21 10:48 11:08 11:28 11:48 12:08 12:28 00:12 Cleaning 10:33 11:00 11:20 11:40 12:20 9:53 10:13 12:00 12:40 00:19 Boarding 00:20 Birmingham 10:12 11:19 12:39 12:59 10:32 10:52 11:39 11:59 12:19 10:07 10:27 10:47 11:07 11:27 11:47 12:07 12:27 12:47 00:49 London 10:56 11:16 11:36 11:56 12:16 12:36 12:56 13:16 13:36

Time Train NO LB403 LB104 LB204 LB303 LB503 LB603 LB703 LB803 LB304 00:06 emptying 00:12 Cleaning 00:19 Boarding 12:42 13:02 13:22 13:42 14:02 14:22 15:22 14:42 15:02 12:54 13:14 13:34 13:54 14:14 14:34 14:54 15:14 15:34 :33 13:33 13:53 14:53 15:33 13:13 14:13 15:13 15:53 00:20 London 13:13 13:33 13:53 14:13 14:33 14:53 15:13 15:33 15:53 00:49 Birmingham 14:02 14:22 14:42 15:02 15:22 15:42 16:02 16:22 16:42 BL703 BL803 BL103 BL203 BL303 BL403 BL504 BL604 BL704 00:06 emptying 00:12 Cleaning Boarding 00:20 Birmingham 12:48 13:08 13:28 13:48 14:08 14:28 14:48 15:08 15:28 13:20 13:40 13:00 14:00 14:20 14:40 15:00 15:20 15:40 14:1 13: 1 1 14:3 14:5 5:1 5:39 5:5 13:07 13:27 13:47 14:07 14:27 14:47 15:07 15:27 15:47 00:49 London 13:56 14:16 14:36 14:56 15:16 15:36 15:56 16:16 16:36

Time Train NO. 00:06 emptying LB404 LB504 LB604 LB704 LB804 LB105 LB205 LB305 LB405 15:42 16:02 16:22 16:42 17:02 17:22 17:42 18:02 18:22 00:12 Cleaning 00:19 Boarding 16:14 16:34 16:54 17:54 18:14 15:54 17:14 17:34 18:34 16:13 16:33 16:53 17:13 17:33 17:53 18:13 18:33 18:53 00:20 London 16:13 16:33 16:53 17:13 17:33 17:53 18:13 18:33 18:53 00:49 Birmingham 17:02 17:22 17:42 18:02 18:22 18:42 19:02 19:22 19:42 BL805 BL804 BL104 BL204 BL304 BL404 BL505 BL605 BL705 00:06 emptying 15:48 16:08 16:28 16:48 17:08 17:28 17:48 18:08 18:28 00:12 Cleaning 00:19 Boarding 16:00 18:20 16:20 16:40 17:00 17:20 17:40 18:00 18:40 16:19 16:39 16:59 17:19 17:59 18:19 18:39 17:39 18:59 00:20 Birmingham 16:07 16:27 16:47 17:07 17:27 17:47 18:07 18:27 18:47 00:49 London 16:56 17:16 17:36 17:56 18:16 18:36 18:56 19:16 19:36

Time Train NO. LB505 LB206 LB306 LB506 LB605 LB705 LB805 LB106 LB406 00:06 emptying 18:42 19:02 19:22 19:42 20:02 20:22 20:42 21:02 21:22 00:12 Cleaning 19:14 19:54 20:54 18:54 19:34 20:14 21:14 21:34 20:34 00:19 Boarding 20:13 20:53 19:13 19:33 19:53 20:33 21:13 21:33 21:53 00:20 London 19:13 19:33 19:53 20:13 20:33 20:53 21:13 21:33 21:53 00:49 Birmingham 22:02 20:02 20:22 20:42 21:02 21:42 22:22 21:22 22:42 BL205 BL305 BL105 BL405 BL506 BL606 BL706 BL806 BL106 00:06 emptying 18:48 19:08 19:28 19:48 20:08 20:28 20:48 21:08 21:28 00:12 Cleaning 19:00 19:20 19:40 20:00 20:20 21:00 21:20 20:40 21:40 00:19 Boarding 19:19 19:39 19:59 20:19 20:39 20:59 21:19 21:39 21:59 00:20 Birmingham 19:07 19:27 19:47 20:07 20:27 20:47 21:07 21:27 21:47 22:16 00:49 London 19:56 20:16 20:36 20:56 21:16 21:36 21:56 22:36

Time Train NO. LB207 LB606 LB706 LB806 LB107 LB307 LB407 00:06 emptying 00:12 Cleaning 00:19 Boarding 22:22 22:42 23:02 21:42 22:02 23:22 23:42 22:14 22:34 21:54 22:54 23:14 23:34 23:54 23:53 22:13 22:33 22:53 23:13 23:33 00:13 00:20 London 22:53 22:13 22:33 23:13 23:33 23:53 00:13 00:49 Birmingham 23:42 23:02 23:22 00:02 00:22 00:42 01:02 BL206 BL306 BL406 BL507 BL607 BL707 BL807 00:06 emptying 00:12 Cleaning 00:19 Boarding 21:48 22:08 22:28 22:48 23:08 23:28 23:48 23:00 23:20 22:00 22:20 22:40 23:40 0:00 23:59 22:19 22:39 22:59 23:19 23:39 0:19 00:20 Birmingham 22:07 22:27 22:47 23:07 23:27 23:47 00:07 00:49 London 23:36 0:16 22:56 23:16 23:56 0:36 0:56