# Okay so Jill is filling the white board with pictures and writing. Amelia is busy erasing all of Jill's hard work. The corner calculates that it takes 15 minutes for the board to be completely...

Okay so Jill is filling the white board with pictures and writing. Amelia is busy erasing all of Jill's hard work. The corner calculates that it takes 15 minutes for the board to be completely erased even with Jill drawing. If it takes Jill 4 minutes longer to fill the board than it takes Amelia o erase it, how long does it take Jill to fill the board without Amelia? how long does it take Amelia to erase it without Jill?

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Let Jill can fill board in x min and Amelia erase board in y min ( when either one is doing their job i.e. not working together)

Jill can fill in 1 min =(1/x) board

Amelia can erase 1 min =(1/y) board

By given condition

In 15 min board will erase

`15(1/y-1/x)=1` (i)

Also

`x=y+4` (ii)

substituting x from (ii) in (i) ,we have

`15(1/y-1/(y+4))=1`

`15{(y+4-y)/(y(y+4))}=1`

`15(4)=y(y+4)`

`y^2+4y=60`

`y^2+4y-60=0`

`y^2+10y-6y-60=0`

`y(y+10)-6(y+10)=0`

`(y-6)(y+10)=0`

`y=6 or y=-10`

`y=-10 ` Not possible.

so y=6 min

x=10 min.

Jill take 10 min to fill board without Amelia.

Amelia take 6 min to erase board without Jill.