$(1\mathrm{.}1$: Modeling$)$ Matt is a software engineer writing a script involving $6$ tasks. Each

must be done one after the other. Let ti be the time needed to complete the ith

task. These times have a certain structure:

$$The total time needed to complete any $3$ adjacent tasks is half the total time

required to complete the next two tasks.

$$The second task takes $1$ second.

$$The fourth task takes $10$ seconds.