1.

A takes 6 hours less than B to complete a work. If together they complete the work in 13 hours 20 minutes, find how much time will B alone take to complete the work.

Answer» Let, B alone completes the work in x hours, then A alone will complete the work in (x-6) hours.
`because(1)/(x-6)+(1)/(x)=(3)/(40)" "(13hr+20min=(40)/(3)hrs.)`
`implies(x+x-6)/((x-6)x)=(3)/(40)`
`implies3x^(2)-18x=80x-240`
`implies3x^(2)-98x+240=0`
`implies3x^(2)-90x-8x+240=0`
`3x(x-30)-8(x-30)=0`
`implies(x-30)(3x-8)=0`
`impliesx=30orx=(8)/(3)`
`impliesx=30" "(ifx=(8)/(3),"then x-6 in negative")` `because` B alone will take 30 hours to complete the work.


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