Let us say the total work is X.
Then the girl takes 90 minutes to do the job and her brother only take 60 minute.
Work done by girl in one minute = (X/90)
Work done by boy in one minute = (X/60)
Let us say when they both work together it take Y minutes.
`Y xx (X/90) + Y xx (X/60) = X`
`(Y/90) + (Y/60) = 1`
`Y = (90 xx 60)/150 = 36 minutes.`
So when they both work together it will take 36minutes.