90 days to build the house
Explanation:It took 45 days to build a house
We need to find the portion of the house that was built in 1 day:
45 days = 1 house
1 day = 1/45 portion of the house
let the number of days it took the second crew to build the house = x
portion of the house built in 1 day by crew 2 = 1/x
Both crew built the house in 30 days
we need to find the portion of the house both crews built in 1 day:
30 days = 1 house
1 day = 1/30 portion of the house
Portion of the house built in 1 day by crew 1 + portion of the house built in 1 day by crew 2 = portion of the house built in 1 day by both crews
[tex]\frac{1}{45}\text{ + }\frac{1}{x}\text{ = }\frac{1}{30}[/tex][tex]\begin{gathered} \frac{x\text{ + 45}}{45x}=\text{ }\frac{1}{30} \\ \text{cross multiply:} \\ 30(x\text{ + 45) = 1(45x)} \end{gathered}[/tex][tex]\begin{gathered} 30(x)\text{ + 30(45) = 45x} \\ 30x\text{ + 1350 = 45x} \\ 1350\text{ = 45x - 30x} \\ 1350\text{ = 15x} \end{gathered}[/tex][tex]\begin{gathered} \frac{1350}{15}=\frac{15x}{15} \\ x\text{ = 90} \end{gathered}[/tex]Working alone, it will take the second crew 90 days to build the house