Question

One crew can build a house in 45 days. With a second crew added a house was built in 30 days. How long would it take the second crew to build a house working alone?

Answer 1

90 days to build the house

Step-by-step 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

`(1)/(45)\text{ + }(1)/(x)\text{ = }(1)/(30)`
`\begin{gathered} \frac{x\text{ + 45}}{45x}=\text{ }(1)/(30) \\ \text{cross multiply:} \\ 30(x\text{ + 45) = 1(45x)} \end{gathered}`
`\begin{gathered} 30(x)\text{ + 30(45) = 45x} \\ 30x\text{ + 1350 = 45x} \\ 1350\text{ = 45x - 30x} \\ 1350\text{ = 15x} \end{gathered}`
`\begin{gathered} (1350)/(15)=(15x)/(15) \\ x\text{ = 90} \end{gathered}`

Working alone, it will take the second crew 90 days to build the house