Question

A person X can clean up all of the crime in a city in 10 hr working alone. Person Y can do the same job alone in 12 hr. If person Y starts crime fighting at 9 A.M. And person X joins him at 10 A.M.​, at what time will they have all the crime cleaned​ up?

Answer 1

They will clean up all the crime at
`3:00` PM.

Explanation:

`X` clean up all crime in
`10\ hr`.

The work done by
`X` is
`1\ hr=(1)/(10)`

`Y` cleanup all crime in
`12\ hr`

The work done by
`Y` in
`1\ hr=(1)/(12)`

`Y` starts at
`9\ AM` and
`X` starts at
`10\ AM`.

let after
`t` hours from
`9:00\ AM` they will finish the work.

`Y` worked for
`t\ hours` and
`X` worked for
`(t-1)\ hours`

`t*(1)/(12)+(t-1)*(1)/(10)=1`

Multiply both side by
`60`

`5t+6(t-1)=60\\11t-6=60\\11t=60+6\\11t=66\\t=6`

Hence they will finish work ofter
`6\ hs`

`=9+6=15:00\ PM`

They both will finish work at
`3:00\ PM`