Question

A takes 6 days less than the time taken by B to finish a piece of work. If both A and B together can finish it in 4 days , find the time taken by B to finish the work.

Answer 1

Heya !!


Let B alone takes X days to finish the work and A alone can finish it in ( X - 6 ) days.



B's 1 day's work = 1/X



A's 1 day's work = 1/(X - 6 )





Therefore,


1/X + 1/X - 6 = 1/4




=> ( X - 6 ) + X / X ( X - 6 ) = 1/4




=> 2X-6/X²-6X = 1 /4




=> X² - 6X = 8X -24



=> X² -14X + 24 = 0



=> X² - 12X - 2X + 24 = 0



=> X ( X - 12 ) - 2 ( X -12 ) = 0





=> ( X - 12 ) ( X - 2 ) = 0




=> X = 12 or X = 2




=> X = 12 [ Since X = 2 => ( X + 6 ) <0 ]



Hence,


B alone can finish the work in 12 days.

Answer 2

We call the time it takes for B to finish the piece of work x.

For problems like these, we must consider how much work can be done in one day.

1x+1x−6=14

x−6x(x−6)+xx(x−6)=14

4(x−6+x)=x2−6x

4(2x−6)=x2−6x

8x−24=x2−6x

0=x2−14x+24

0=(x−12)(x−2)

x=12and2

If the time it takes B is 2 days, then the time it takes Ais −4 days, which has no sense.

Therefore, it would take B a period of 12 days to finish the job.

Hopefully this helps!