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A group of 5 boys booked a badminton court for 2 hours and took turns to play. At any time, there were 4 boys playing on the court. On average, how long did each boy play on the court?Give your answer in hours and minutes.

This was 2-mark question that doesn’t fall neatly under any particular Primary School syllabus topic or heuristics category. The main concept which this question tests is ‘average’. The question looks deceptively simple, yet, many students whom we posed this question to struggled with it.

One of the first questions that students tend to ask is this: did the 5 boys get equal time on the court? Frankly, we can’t tell from the information given in the question alone. All we know is they “took turns”. Fortunately, we don’t need to know the answer to that because the question requires us only to find out the “average” duration. And average duration means that individual timings do not matter as long as we know the total time*.

Method 1

Let’s assume every student spent the same amount of time on the court (which is the average time anyway). For this to happen, the order of play needs to follow the sequence below.

Session 1: Student A, Student B, Student C, Student D

Session 2: Student B, Student C, Student D, Student E

Session 3: Student C, Student D, Student E, Student A

Session 4: Student D, Student E, Student A, Student B

Session 5: Student E, Student A, Student B, Student C

We can stop at session 5 because the students who would be playing in session 6 would be the same as those playing in session 1.

Since the total duration is 2 hours (120 minutes),

the duration of each session = 120 min ÷ 5 = 24 min

From the list above, we can see that each student played in 4 of the 5 sessions.

Thus, average time each student spent on the court = 24 min x 4 = 1 hour 36 min

Method 2

4 students can play on the court at any one time.

Assuming the 5th student didn’t get to play at all, then each of the lucky 4 students played for a full 2 hours (120 minutes).

Thus, the cumulative time spent on the court by the 4 students = 4 x 120 min = 480 min.

Dividing that equally among 5 students, we have = 480 min ÷ 5 = 1 h 36 min

*Consider the following scenarios.

Scenario A:

4 students played for 120 minutes and 1 student played for 0 minutes.

Average duration = 120 minutes/5 = 24 minutes.

Scenario B:

All 5 students spent equal time on the court.

Average duration = 120 minutes/5 = 24 minutes.

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