Question

Working alone it takes Ryan 13.4 weeks to build a home.Jack can build the same home in 13.1 weeks how long would it take them if they work together

Answer 1

Answer: 6.62 weeks

Step-by-step explanation:

Time taken by Ryan to build a home = 13.4 weeks

Time taken by Jack to build the same home = 13.1 weeks

Let t be the time to complete a house if they work together, then

$\frac{1}{t}=\frac{1}{t}$= $\frac{1}{\text{time taken by Ryan alone}}+\frac{1}{\text{time taken by Jack alone}}$

$=\frac{1}{13.4}+\frac{1}{13.1}\\\\=\frac{13.1+13.4}{175.54}\\\\=\frac{26.5}{175.54}$

$\\\Rightarrow\ t=\frac{175.54}{26.5}\\\Rightarrow\ t=6.62\ weeks$