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 70 seconds. The difference between the time taken by David and Cole was 6 seconds. Find the longest possible time taken by Rael.
Total time of 4 participants
= 4 x 70
= 280 s

Total time taken by David, Rael and Cole
= 280 - 65
= 215 s

Comparing the time taken by David and Cole:
Time taken by the slower runner: 1 u + 6
Time taken by the faster runner: 1 u

Total time taken by David and Cole
= 1 u + 6 + 1 u
= 2 u + 6

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

Scenario 1
Time taken by David and Cole if the time taken by Rael was 89 s
= 215 - 89
= 126 s

2 u + 6 = 126
2 u = 126 - 6
2 u = 120

1 u = 120 ÷ 2 = 60 (✓) (Possible as all the times recorded are whole numbers.)

Time taken by Rael = 89 s

Answer(s): 89 s