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Average speed · round trip

P6 · Speed · PSLE Maths

Question

Siti cycled from her home to East Coast Park and returned along the same route. Her speed was 18 km/h on the way there and 12 km/h on the way back. What was her average speed for the whole journey?

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Hint

Average speed = total distance ÷ total time. Do not simply average 18 and 12; you may assume the one-way distance is 36 km.

Show the answer and step-by-step explanation

Answer: Average speed 14.4 km/h

  1. Draw distances — The way there and the way back are along the same route, so the two distances are equal. Draw two bars of the same length.
  2. Choose distance — It is fine that the actual distance is not given. Since the distances are equal, choose a convenient one-way distance: 36 km, which is divisible by both 18 and 12.
  3. Find time — Time = distance ÷ speed. There: 36 ÷ 18 = 2 h; Back: 36 ÷ 12 = 3 h.
  4. Put together — Average speed uses total distance ÷ total time. The total distance is 72 km and the total time is 5 h.
  5. Find average — Average speed = 72 ÷ 5 = 14.4 km/h. Be careful: it is not (18 + 12) ÷ 2, because the times taken are different. 📌 Key idea: for a round trip over the same distance, find total distance and total time first.

Method: For a round trip over the same route, the two distances are equal. Choose a convenient one-way distance, find each time, then divide the total distance by the total time.

Practice: 3 similar questions

  1. Raju cycled from home to the community library and returned along the same route. His speed was 15 km/h on the way there and 10 km/h on the way back. What was his average speed for the whole journey?
    Answer

    12 km/h — Assume the one-way distance = 30 km. Time there = 30 ÷ 15 = 2 h; time back = 30 ÷ 10 = 3 h. Total distance = 60 km, total time = 5 h. Average speed = 60 ÷ 5 = 12 km/h.

  2. Mei Ling took a bus from school to a museum and returned to school along the same route. The bus travelled at 40 km/h on the way there and 60 km/h on the way back. What was the average speed for the whole journey?
    Answer

    48 km/h — Assume the one-way distance = 120 km. Time there = 120 ÷ 40 = 3 h; time back = 120 ÷ 60 = 2 h. Total distance = 240 km, total time = 5 h. Average speed = 240 ÷ 5 = 48 km/h.

  3. A school coach travelled from school to a sports hall and returned along the same route. Its speed on the way there was 30 km/h, and its average speed for the whole journey was 24 km/h. What was its speed on the way back?
    Answer

    20 km/h — Assume the one-way distance = 120 km, so the total distance = 240 km. The average speed for the whole journey is 24 km/h, so total time = 240 ÷ 24 = 10 h. Time there = 120 ÷ 30 = 4 h. Time back = 10 − 4 = 6 h. Speed back = 120 ÷ 6 = 20 km/h.

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