Question

Dal and Kim can assemble a swing set in 1/1/2 hrs,working alone it takes Kim 4 hrs longer than Dal to assemble the swing set.How long would it take Dal to working alone to assemble the set

Answer 1

Dal takes d
Kim takes k
Dal&Kim take b (for both)

1/b = 1/d + 1/k
1/(3/2) = 1/d + 1/(d+4)

2/3 = 1/d + 1/(d+4)
multiply through by 3d(d+4) to get
2d(d+4) = 3(d+4) + 3d
2d^2 + 8d = 3d + 12 + 3d
2d^2 + 2d - 12 = 0
d^2 + d - 6 = 0
(d+3)(d-2) = 0

d = -3 or 2

must have positive time, so d=2

That is, Dal takes 2 hours by himself

check:
1/2 + 1/6 = 2/3 = 1/(3/2)