Daniel and Billy take 4 days to assemble a toy house. Billy and Vincent take 4 days to build the same house while Daniel and Vincent take only 5 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 Daniel and Billy per day
= ¹₄ P

Fraction of the house assembled by Vincent and Billy per day
= ¹₄ P

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

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

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

Answer(s): 3 days