Question

Batman can clean up all of the crime in Gotham City in 8 hours working alone. Robin can do the same job alone in 12 hours. If Robin starts crime fighting at 8:00 AM and Batman joins him at 10:00 AM, then at what time will they have all of the crime cleaned up

Answer 1

The crime gets cleaned up at 2:00 PM

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.

$\texttt{Rate of batman,}r_b=\frac{W}{8}$

Robin can do the same job alone in 12 hours.

$\texttt{Rate of Robin,}r_r=\frac{W}{12}$

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

                             $t\times \frac{W}{8}+(t+2)\times \frac{W}{12}=W\\\\12t+8t+16=96\\\\20t=80\\\\t=4hours$

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