Albert and Vincent take 2 days to assemble a toy house. Vincent and Ian take 5 days to build the same house while Albert and Ian take only 2 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 Albert and Vincent per day
= ¹₂ P

Fraction of the house assembled by Ian and Vincent per day
= ¹₅ P

Fraction of the house assembled by Albert and Ian per day
= ¹₂ P

Combined rate
= (¹₂ + ¹₅ + ¹₂) ÷ 2
= (⁵₁₀ + ²₁₀ + ⁵₁₀) ÷ 2
= ¹²₁₀  ÷ 2
= ¹²₁₀  x ¹₂
= ³₅ P 

Number of days taken by the three of them to build the same toy house
= 1 ÷ ³₅
= 1 x ⁵₃
= 1.67

Since the number of days needed is 1.67 days, therefore the total number of complete days needed to build the toy house is 2.

Answer(s): 2 days