Working together, Bill and Tom painted a fence in 8 hours?

Question

Working together, Bill and Tom painted a fence in 8 hours. Last year, Tom painted the fence by himself. The year before, Bill painted it by himself, but it took 12 hours less than Tom took. How long did Bill and Tom take when each was painting alone.

Answer 1

This might not be the easiest way to do this but it works......

You have 3 equations

8B(ill) + 8T(om) = F (man hours to paint fence) (1)

xT=F (2)

(x-12)B=F (3)

Rearrange 2 and 3 for T and B and replace T and B in 1 gives

8F/(x-12) + 8F/x = F

cancel the F's

8/(x-12) + 8/x = 1

Multiply the whole equation by x(x-12) gives

8x +8(x-12) = x(x-12)

A little rearranging gives you a quadratic

x^2 - 28x +96 = 0

Solve this to give x= 4 or 24

A little thought shows 4 is incorrect (as then Bill could do it in negative time)

Therefore Tom does it in 24 hours Bill in 12 - check this to the first equation to reassure yourself.

Answer 2

It took Tom 14, and Bill 2 hours.

Answer 3

a thanks to unravel those is to apply fractions. Dave can do a million/6 of the pastime in an hour. Tom can do a million/4 of the pastime in an hour. once you upload both up, you get a million/x and the x is what percentage hours you'll want. So: a million/6 +a million/4= ? person-friendly denominator: 4/24 + 6/24 = a million/x 10/24=a million/x flow multiply to get: 10x=24 So, x ought to equivalent 2.4.