PA $8-4($Algo$)$ In the welding operations of a bicycle manufacturer...

In the welding operations of a bicycle manufacturer, a bike frame has a flow time of about $13\mathrm{.}6$ hours. The time in the welding operation

is spent as follows: $3$ hours waiting in front of the cutting machine for the batch to start, $3$ hours waiting for the setup of the machine, $1$

hour waiting for the other pieces of the batch to go through cutting, $2$ minutes at the cutting machine, and $3$ hours waiting for the

transfer to the welding machine. Then, at the welding machine, the unit spends $1$ hour waiting in front of the welding machine for the

batch to start, $1$ hour waiting for the setup of the welding machine, $0\mathrm{.}6$ hours waiting for the other pieces of the batch to go through

welding, $0\mathrm{.}65$ minutes at the welding machine, and $1$ hour waiting for the transfer to the next department.

Determine the exact flow time. What is the value$-$added percentage of the flow time?

Note: Round your percentage answer to $4$ decimal places.