#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, how many days will #B# take to finish the work?

Question

Isaiah Anthony · Accepted Answer

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

We have to think about how much work can be done in a day when dealing with problems like these.

#1/x + 1/(x- 6) = 1/4#

#(x - 6)/(x(x - 6)) + x/(x(x - 6)) = 1/4#

#4(x - 6 + x) = x^2 - 6x#

#4(2x- 6) = x^2 - 6x#

#8x - 24 = x^2 - 6x#

#0 = x^2 - 14x + 24#

#0 = (x- 12)(x - 2)#

#x = 12 and 2#

If the time it takes #B# is #2# days, then the time it takes #A# is #-4# days, which has no sense.

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

I hope this is useful!

Isaiah Anthony · Answer

undefined Let the time taken by B to finish the work be $ x $ days.
Then, A takes $ x - 6 $ days to finish the work.
Their combined rate of work is $ \frac{1}{x} + \frac{1}{x-6} = \frac{1}{4} $.
Solving this equation, we find that $ x = 12 $ days.
So, B takes 12 days to finish the work.