Ryan and Luke take 4 days to assemble a toy house. Luke and Owen take 6 days to build the same house while Ryan and Owen take only 3 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 Ryan and Luke per day
= ¹₄ P

Fraction of the house assembled by Owen and Luke per day
= ¹₆ P

Fraction of the house assembled by Ryan and Owen per day
= ¹₃ P

Combined rate
= (¹₄ + ¹₆ + ¹₃) ÷ 2
= (³₁₂ + ²₁₂ + ⁴₁₂) ÷ 2
= ⁹₁₂  ÷ 2
= ⁹₁₂  x ¹₂
= ³₈ P 

Number of days taken by the three of them to build the same toy house
= 1 ÷ ³₈
= 1 x ⁸₃
= 2.67

Since the number of days needed is 2.67 days, therefore the total number of complete days needed to build the toy house is 3.

Answer(s): 3 days