$1)$ The first unit took $79$ hours; the tenth took $46$ hours. What learning rate is implied by the data?

$2)$ Your firm has expertise with a special type of hand$-$finished furniture. The learning rate is known to be $82\%.$ If the first piece of furniture took $6$ hours, how long will it take to do the second? How long will it take to do the fourth?

$3)$ You are about to undertake manufacture of a labour$-$intensive electronics component. The first unit took $300$ hours. You are not sure whether the learning rate is $70\%$ or $80\%.$ The initial phase of the contract calls for $6$ of these components.

a$.$ How much time will it take to complete all six at $70\%$ learning?

b$.$ How much time will it take to complete all six at $80\%$ learning?

$4)$ The fourth unit of production took $80$ minutes while the ninth unit of production took $50$ minutes. How long did the first unit take?