Answer
23.5 minutes
Work Step by Step
Mike takes 75 minutes, Joan takes 60 minutes, Kyle takes 80 minutes
$x/75 + x/60 + x/80 = 1$
$3600*(x/75 + x/60 + x/80 = 1)$
$3600x/75 + 3600x/60 + 3600x/80 = 3600$
$48x + 60x+45x = 3600$
$153x = 3600$
$153x/153 = 3600/153$
$x = 23.5$