The charges are :
$17 fixed charge plus an additional $6 per every hour of renting
Taking h as the number of hours taken for renting the bike, then an equation for total cost of renting the bike will be,
c=$17 + $6h -------- where c is the total cost
Given that the cost Tim paid is $59 then use the equation to get the hours he check out as;
c=$17+ $6h
$59 = $17 + $6h
collect like terms as;
$59 - $ 17 = $6h
$ 42 = $ 6h
42 = 6h
42/6 = h
7 = h
So the number of hours Tim check out the bike is 7 hours.
