Step-by-step explanation:
Let the work be w.
Batman can clean up all of the crime in Gotham City in 8 hours working alone.
[tex]\texttt{Rate of batman,}r_b=\frac{W}{8}[/tex]
Robin can do the same job alone in 12 hours.
[tex]\texttt{Rate of Robin,}r_r=\frac{W}{12}[/tex]
Robin starts work at 8:00 AM and Batman Joins at 10:00 AM.
Let the time of completion of work after Batman's joining be t.
We have time of working of Robin = t + 10:00 -8:00 = t + 2
So
[tex]t\times \frac{W}{8}+(t+2)\times \frac{W}{12}=W\\\\12t+8t+16=96\\\\20t=80\\\\t=4hours[/tex]
After 4 hours of 10:00 Am work gets completed.
Time = 10:00 AM + 4 hours = 2:00 PM
The crime gets cleaned up at 2:00 PM
