Xavier and Valen take 5 days to assemble a toy plane. Valen and Caden take 4 days to build the same plane while Xavier and Caden 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 Xavier and Valen per day
= ¹₅ P

Fraction of the plane assembled by Caden and Valen per day
= ¹₄ P

Fraction of the plane assembled by Xavier and Caden per day
= ¹₄ P

Combined rate
= (¹₅ + ¹₄ + ¹₄) ÷ 2
= (⁴₂₀ + ⁵₂₀ + ⁵₂₀) ÷ 2
= ¹⁴₂₀  ÷ 2
= ¹⁴₂₀  x ¹₂
= ⁷₂₀ P 

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

Answer(s): 3 days