Next time the clock hands coincide after noon

The hour and minute hands of a clock overlap exactly at $12{:}00$ noon. How many hours later will they next overlap? Give a fraction if needed.

$12/11$ hours (about $1{:}05{:}27$). The minute hand gains $330^\circ$ per hour on the hour hand, and it must gain a full $360^\circ$, so $t=\tfrac{360}{330}=\tfrac{12}{11}$.