Pierre and Jack take 6 days to assemble a toy house. Jack and Cole take 3 days to build the same house while Pierre and Cole take only 5 days. How many complete days would the three of them take to build the same toy house?
Let the house be 1 P.

Fraction of the house assembled by Pierre and Jack per day
= ¹₆ P

Fraction of the house assembled by Cole and Jack per day
= ¹₃ P

Fraction of the house assembled by Pierre and Cole per day
= ¹₅ P

Combined rate
= (¹₆ + ¹₃ + ¹₅) ÷ 2
= (⁵₃₀ + ¹⁰₃₀ + ⁶₃₀) ÷ 2
= ²¹₃₀  ÷ 2
= ²¹₃₀  x ¹₂
= ⁷₂₀ P 

Number of days taken by the three of them to build the same toy house
= 1 ÷ ⁷₂₀
= 1 x ²⁰₇
= 2.86

Since the number of days needed is 2.86 days, therefore the total number of complete days needed to build the toy house is 3.

Answer(s): 3 days