Perry and Xavier take 3 days to assemble a toy train. Xavier and Andy take 6 days to build the same train while Perry and Andy take only 5 days. How many complete days would the three of them take to build the same toy train?
Let the train be 1 P.

Fraction of the train assembled by Perry and Xavier per day
= ¹₃ P

Fraction of the train assembled by Andy and Xavier per day
= ¹₆ P

Fraction of the train assembled by Perry and Andy per day
= ¹₅ P

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

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

Answer(s): 3 days