1.9.5 Video task: Planning specials
Now watch the video.
Video, Click to watch part three
Transcript: Singletrack minders  Part 3
Activity: 25 Planning a special
A special train has been booked to take a party from Bridgnorth to Kidderminster. Use your distancetime graph to plan an extra train that will leave Bridgnorth at 11.13 am, cross the service train at Hampton Loade and wait there for 30 minutes. It is then to continue nonstop to Kidderminster, crossing with the service train at Bewdley.

When should the train reach Bewdley?

What should be its average speed between Hampton Loade and Bewdley?

What time should it arrive at Kidderminster, assuming it maintains a constant speed from Hampton Loade?
Discussion

To cross the service train without stopping, it should pass through Bewdley just after AN1 arrives at 12.56 am. Scheduling the cross at 12.57 would leave a little time for AN1 to arrive.

If the train leaves Hampton Loade at 12.00 and passes through Bewdley at 12.57, it will have covered 12.8 km in 57minutes. Its average speed will be (12.8/57)×60=13.5 km per hour.

From the graph or by calculation, the train should reach Kidderminster just after 1.16pm.
Video, Click to watch part four
Transcript: Singletrack minders  Part 4
Activity 26: Timetabling a Santa Special
At Christmas, Santa Special trains run between Kidderminster and Arley. The service runs every 30 minutes, leaving Kidderminster at 15 and 45 minutes past the hour.
Figure 58 shows the positiontime graphs of two Santa Special trains. Between these trains two more trains run to complete the service.
Draw in the graph for the train that leaves Kidderminster at 11.15 am. It runs at exactly the same speed as the 10.45 and the 11.45 trains. Trains can cross just outside Kidderminster.

When does it arrive at and depart from Bewdley?

At what time will it reach Arley?
Draw in the graph for the train that arrives at Kidderminster at 11.46 am.

When does it arrive at and depart from Bewdley?

At what a time does it leave Arley?

Could another service be fitted in so that trains at 15minute intervals?
Make a few notes to explain how you obtained your answer.
Discussion
Figure 60 shows the graphs for all the Santa Specials between the given times. Notice that the graph for the 11.15 from Kidderminster is the same as the graph for the 10.45, only shifted along by thirty minutes. Similarly, the 11.46 arrival at Kidderminster has the same graph as the 11.16 arrival, but shifted forward by thirty minutes.

The 11.15 from Kidderminster arrives at Bewdley at 11.25 am, and departs at 11.30 am.

It will arrive at Arley at 11.42 am.

The 11.46 arrival at Kidderminster arrives at Bewdley at 11.29 am and leaves Bewdley at 11.35 am.

It leaves Arley at 11.14 am.

To run a fifteenminute service, extra trains would have to leave Kidderminster at 11.00am (and 11.30am). But these trains would have to cross the 11.05 (and 11.35) trains from Bewdley. Since there is no crossing place between Bewdley and Kidderminster, the extra trains cannot run.