3 A team triathlon is a race involving swimming, cycling and running for teams of three people. The first person swims, then the second person cycles and finally the third person runs. The winning team is the team that completes all three stages of the triathlon in the shortest time.
Four friends are training to enter as a team for the triathlon. They need to choose who to enter for each stage of the triathlon, and who to leave out (this person will be the reserve). The table shows the times, in minutes, for each of them to complete each stage in training.
| Swim | Cycle | Run |
| Fred | 30 | 75 | 48 |
| Gary | 25 | 82 | 45 |
| Helen | 45 | 76 | 53 |
| Isobel | 40 | 70 | 45 |
- Complete a dummy column in the table in your answer book. Apply the Hungarian algorithm, reducing columns first. Make sure that the values in your tables can all be seen. Write a list showing who should be chosen for each stage of the triathlon. What is the minimum total time in which the team can expect to complete the three stages of the triathlon?
The day before the triathlon, the friend who had been chosen to swim is injured and cannot compete.
- If the reserve takes over the swim, how much longer can the team expect the triathlon to take?
- Remove the row corresponding to the injured swimmer to form a \(3 \times 3\) table. Apply the Hungarian algorithm to find who should be chosen for each stage to complete the triathlon in the minimum expected time. State the minimum expected time.