The table shows the time taken by 4 participants in a race. All the times recorded are in whole numbers. Some of the time recorded were blocked by an ink drop. The average time taken by the 4 participants was 69 seconds. The difference between the time taken by Oscar and Tom was 7 seconds. Find the longest possible time taken by John.
Total time of 4 participants
= 4 x 69
= 276 s

Total time taken by Oscar, John and Tom
= 276 - 66
= 210 s

Comparing the time taken by Oscar and Tom:
Time taken by the slower runner: 1 u + 7
Time taken by the faster runner: 1 u

Total time taken by Oscar and Tom
= 1 u + 7 + 1 u
= 2 u + 7

To find the longest possible time taken by John, the time taken by him must be as high as possible and a whole number.

Scenario 1
Time taken by Oscar and Tom if the time taken by John was 99 s
= 210 - 99
= 111 s

2 u + 7 = 111
2 u = 111 - 7
2 u = 104

1 u = 104 ÷ 2 = 52 (✓) (Possible as all the times recorded are whole numbers.)

Time taken by John = 99 s

Answer(s): 99 s