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 75 seconds. The difference between the time taken by Ivan and Glen was 3 seconds. Find the shortest possible time taken by Billy.
Total time of 4 participants
= 4 x 75
= 300 s

Total time taken by Ivan, Billy and Glen
= 300 - 85
= 215 s

Comparing the time taken by Ivan and Glen:
Time taken by the slower runner: 1 u + 3
Time taken by the faster runner: 1 u

Total time taken by Ivan and Glen
= 1 u + 3 + 1 u
= 2 u + 3

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

Scenario 1
Time taken by Ivan and Glen if the time taken by Billy was 80 s
= 215 - 80
= 135 s

2 u + 3 = 135
2 u = 135 - 3
2 u = 132

1 u = 132 ÷ 2 = 66 (✓) (Possible as all the times recorded are whole numbers.)

Time taken by Billy = 80 s

Answer(s): 80 s