Answer:
They will clean up all the crime at [tex]3:00[/tex] PM.
Step-by-step explanation:
[tex]X[/tex] clean up all crime in [tex]10\ hr[/tex].
The work done by [tex]X[/tex] is [tex]1\ hr=\frac{1}{10}[/tex]
[tex]Y[/tex] cleanup all crime in [tex]12\ hr[/tex]
The work done by [tex]Y[/tex] in [tex]1\ hr=\frac{1}{12}[/tex]
[tex]Y[/tex] starts at [tex]9\ AM[/tex] and [tex]X[/tex] starts at [tex]10\ AM[/tex].
let after [tex]t[/tex] hours from [tex]9:00\ AM[/tex] they will finish the work.
[tex]Y[/tex] worked for [tex]t\ hours[/tex] and [tex]X[/tex] worked for [tex](t-1)\ hours[/tex]
[tex]t\times\frac{1}{12}+(t-1)\times\frac{1}{10}=1[/tex]
Multiply both side by [tex]60[/tex]
[tex]5t+6(t-1)=60\\11t-6=60\\11t=60+6\\11t=66\\t=6[/tex]
Hence they will finish work ofter [tex]6\ hs[/tex]
[tex]=9+6=15:00\ PM[/tex]
They both will finish work at [tex]3:00\ PM[/tex]
