The Sun Belt has a receivables turnover rate of $13\mathrm{.}1,$ a payables turnover rate of $8\mathrm{.}7,$ and an inventory turnover rate of $12\mathrm{.}4.$ What is the length of the firm's operating cycle?

a$.$

$38\mathrm{.}87$ days

b$.$

$62\mathrm{.}27$ days

c$.$

$25\mathrm{.}50$ days

d$.$

$57\mathrm{.}30$ days

e$.$

$41\mathrm{.}41$ days