Employee daily schedule Gantt chart

This proposed solution employs helper columns which may be moved and/or hidden for aesthetic purposes.
On the 'Mon' sheet the helper column is AE which is populated using the formula: =D5<C5
The conditional formatting rule for the 'Mon' sheet, which is only applied to rows 5 and 6 so far, is:

Formula:

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Also added to the 'Mon' sheet is a formula to populate column E: =(D5+(D5<C5)-C5)*24
On both the 'Mon' and 'Tues' sheets times in the 'In' and 'Out' columns have been input as actual time formatted h:mm AM/PM
Likewise times in row 3 have been input as actual times formatted h AM/PM
On the 'Tues' sheet one helper column is C which is populated using the formula: =IF(Mon!AE5=TRUE,Mon!D5,"")
Column AF on the 'Tues' sheet is populated using: =E5<D5
There are two conditional formatting rules for the 'Tues' sheet.
The first is:

Formula:

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The second is: =IF($C5<>"",H$3<=$C5)
Also added to the 'Tues' sheet is a formula to populate column F: =(E5+(E5<D5)-D5)*24
Formulas will need to be copied down each sheet and the range for the conditional formatting rules will need to be expanded.
The sheets for the rest of the week will need to be set up like the 'Tues' sheet.
Let us know if you have any questions.