A cyclist rides 10km. In the first 5km, they climb a hill, averaging 10km/h. In the second 5km, they descend the hill, averaging 30km/h. What is their average speed over the full 10km?
A common response from the student for the above question is: “I got 20km/h but it says it’s wrong! help i’m really confused”. The following two paragraphs will outline how I might attempt explain this idea to the student in a clear and positive way, including the working for my answer. Paragraph 1 Start by introducing myself to the student and ask the student the following questions first: • Are you familiar with the formulae for motion? Then based on the reply of the student, establish the fact that "Average Speed = (Total Distance) / (Total time)" Then ask the student the following question: • So, in this case, do we know the total distance travelled by the cyclist? Hint: Read the question, it is given there! :) Then based on the reply of the student, establish the fact that the total distance = 10 km Then ask the student the following question: • Do we know the total time taken by the cyclist to travel this distance? Then based on the reply of the student, establish that the total time taken is not given in the question and that we actually need to calculate it by ourselves. Hint: We need to find the time taken to complete both the first part of the journey and also the second part of the journey respectively using our basic equation of motion. So for the first part of the journey, distance travelled = 5km, and Average Speed was 10 km/hr. Then ask the student the following question: • So how can we determine the time taken for this part? Hint: Average Speed = (Total Distance) / (Total time) Discuss with the student and establish that “Total time = total distance/ average speed” Ensure that the student is independently able to determine that, the time for the first part of the journey, “t1” = (5km) / (10 km/h) = 0.5 h Paragraph 2 Ask the student again the following question: • Can we find the time taken to complete the second part of the journey ? Hint: It is in fact similar to the first part of the journey. So for the first part of the journey, distance travelled = 5km, and Average Speed was 30 km/h. If the student is still unable to proceed, then follow up with the following question: • So how can we determine the time taken for this part? Hint: Average Speed = (Total Distance) / (Total time) Ensure that the student is independently able to determine that, the time for the second part of the journey, “t2” = (5km) / (30 km/h) = 1/6 h We now know the time required for both parts of the journey. Ask the question the following question: • So can we find the total time? Then based on the reply of the student, establish the fact that the total time = t1 + t2 = 0.5h +1/6h = 2/3 h Now that we now know the total distance travelled and the total time taken for the entire journey. Finally ask the student the following question: • So what will be the average speed? Ensure that the student is independently able to establish that average speed = 10 km / {(2/3) h} = 15 km/h
