A railway line has three stations, Town, Port and Cove.
Train A leaves Town for Cove and train B leaves Cove for Town.
Both trains stop at Port.
(a) Write down the time that train B leaves Cove.
(b) Write down how long train A stops at Port.
(c) How many more minutes does train A take to complete the whole journey than train B?
(d) Write down the time that the two trains pass each other.
(e) Work out the average speed of train A between Town and Cove in kilometres per hour.
▶️ Answer/Explanation
(a) 14:10
From the graph, train B’s departure time from Cove is clearly marked as 14:10.
(b) 4 minutes
Train A arrives at Port at 14:20 and departs at 14:24, so the stop time is 4 minutes.
(c) 2 minutes
Train A takes 40 minutes (14:00-14:40), train B takes 38 minutes (14:10-14:48). The difference is 2 minutes.
(d) 14:25
The trains pass each other at the point where their lines cross on the graph, which is at 14:25.
(e) 34.5 km/h
Total distance is 23 km, time taken is 40 minutes (2/3 hours). Speed = distance/time = 23/(2/3) = 34.5 km/h.
(a) The diagram shows the travel graph of a train journey from Wengen to Kleine Scheidegg.
(i) Explain what happens between 14.09 and 14.10.
(ii) Find the journey time from Allmend to Wengemalp in minutes.
(iii) Calculate the average speed for the train journey from Wengen to Kleine Scheidegg. Give your answer in km/h.
(iv) Another train travels from Kleine Scheidegg to Wengen.
The table gives information about its journey.
On the travel graph, draw the journey for this train.
(v) Write down the time when the two trains pass each other.
(b) The temperature in Wengen at 5 am was −3°C.
At 4 pm the temperature has increased by 10°C.
Work out the temperature at 4 pm.
(c) A formula to work out the temperature at different heights above Wengen is
\( T = 2 – \frac{h}{130} \)
where \( T \) is the temperature in °C and \( h \) is the height, in metres, above Wengen.
Kleine Scheidegg is 780 m above Wengen.
Work out the temperature at Kleine Scheidegg.
▶️ Answer/Explanation
(a)(i) The train stops between 14.09 and 14.10.
(a)(ii) 10 minutes (from 14.10 to 14.20).
(a)(iii) 15.36 km/h. Total distance is 6.4 km and time taken is 25 minutes (0.4167 hours). Speed = distance/time = 6.4/0.4167 ≈ 15.36 km/h.
(a)(iv) Draw lines: from (1401, 6.4) to (1418, 1.9), then horizontal to (1420, 1.9), then to (1430, 0).
(a)(v) 14:09 (when the two trains meet).
(b) 7°C. -3°C + 10°C = 7°C.
(c) -4°C. Substitute h = 780 into the formula: T = 2 – (780/130) = 2 – 6 = -4°C.