Champion Cooling has just signed a contract to assemble window air conditioners for another company. The list of tasks, including time requirements and immediate predecessors, follows. Each task may not be shortened. The plan is to make $300$ units in an eight hour day. What should their takt time be$?$

$\backslash$table$[[$Task$,$Time $($min$),$Predecessor$],[$Bolt compressor to base,$5,$None$],[$Install coils and lines,$6,$Bolt compressor to base$],[$Install fan motor,$7,$Install coils and lines$],[$Install switch and thermostat,$5,$Install fan motor$],[$Charge system and test,$10,$Install switch and thermostat$],[$Cosmetic detailing,$7,$Charge system and test$]]$