Nick and Ivan take 3 days to assemble a toy plane. Ivan and Ethan take 6 days to build the same plane while Nick and Ethan take only 4 days. How many complete days would the three of them take to build the same toy plane?
Let the plane be 1 P.

Fraction of the plane assembled by Nick and Ivan per day
= ¹₃ P

Fraction of the plane assembled by Ethan and Ivan per day
= ¹₆ P

Fraction of the plane assembled by Nick and Ethan per day
= ¹₄ P

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

Number of days taken by the three of them to build the same toy plane
= 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 plane is 3.

Answer(s): 3 days