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

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=(W)/(8)`

Robin can do the same job alone in 12 hours.

`\texttt{Rate of Robin,}r_r=(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* (W)/(8)+(t+2)* (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