It is $4:00$ now. How many minutes does it take for the clock\textquotesingle s hour and minute hands to overlap for the first time? 
选项为:A:$43\frac 7{11}$ minutes  B:$10\frac {10}{11}$ minutes  C:$21\frac 9{11}$ minutes  D:$22\frac 9{11}$ minutes  E:$42\frac 7{11}$ minutes  请回答其中一个选项.