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 72 seconds. The difference between the time taken by Glen and Asher was 4 seconds. Find the longest possible time taken by Julian.
Total time of 4 participants
= 4 x 72
= 288 s

Total time taken by Glen, Julian and Asher
= 288 - 79
= 209 s

Comparing the time taken by Glen and Asher:
Time taken by the slower runner: 1 u + 4
Time taken by the faster runner: 1 u

Total time taken by Glen and Asher
= 1 u + 4 + 1 u
= 2 u + 4

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

Scenario 1
Time taken by Glen and Asher if the time taken by Julian was 99 s
= 209 - 99
= 110 s

2 u + 4 = 110
2 u = 110 - 4
2 u = 106

1 u = 106 ÷ 2 = 53 (✓) (Possible as all the times recorded are whole numbers.)

Time taken by Julian = 99 s

Answer(s): 99 s