How many hours each employee should work to get to a certain percentage of total hrs

I am trying to come up with a formula that will calculate how many hours each employee should work to get to a certain percentage of the total hours worked, while keeping the costs at a certain dollar amount.

Basically:
Total budget = $100k
Mike's hourly rate = $45/hr
Sean's hourly rate = $39/hr
Mike needs to work 40% of the total hours
Sean needs to work 60% of the total hours
The total cost must be $100k

How many hours is each employee working?

I attached a spreadsheet that should explain more clearly what I'm looking for.

I would really appreciate any help! Thanks in advance!

Try: =$B$3*$F17/$B17

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I did it for you this time