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 74 seconds. The difference between the time taken by Eric and Owen was 7 seconds. Find the shortest possible time taken by Justin.
Total time of 4 participants
= 4 x 74
= 296 s

Total time taken by Eric, Justin and Owen
= 296 - 76
= 220 s

Comparing the time taken by Eric and Owen:
Time taken by the slower runner: 1 u + 7
Time taken by the faster runner: 1 u

Total time taken by Eric and Owen
= 1 u + 7 + 1 u
= 2 u + 7

To find the shortest possible time taken by Justin, the time taken by him must be as low as possible and a whole number.

Scenario 1
Time taken by Eric and Owen if the time taken by Justin was 90 s
= 220 - 90
= 130 s

2 u + 7 = 130
2 u = 130 - 7
2 u = 123

1 u = 123 ÷ 2 = 61.5 (x)  (Not possible as all the times recorded are whole numbers.)

Scenario 2
Time taken by Eric and Owen if the time taken by Justin was 91 s
= 220 - 91
= 129 s

2 u + 7 = 129
2 u = 129 - 7
2 u = 122 

1 u = 122 ÷ 2 = 61 (✓) (Possible as all the times recorded are whole numbers.)

Time taken by Justin = 91 s

Answer(s): 91 s