Question

Sam takes 4 hours to paint a house and Rita takes 6 hours to paint the same house. How much time time do they take to paint the house together ?

the ans. is 2hrs and 24min. But how to solve it??

Answer 1

$$\begin{gathered} \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Sam}\mathrm{to}\mathrm{paint}\mathrm{a}\mathrm{house}=4\mathrm{hrs} \\ \mathrm{Sam}\text{'}\mathrm{s}1\mathrm{hour}\text{'}\mathrm{s}\mathrm{work}=\frac{1}{4} \\ \mathrm{Time}\mathrm{taken}\mathrm{by}\mathrm{Rita}\mathrm{to}\mathrm{paint}\mathrm{a}\mathrm{house}=6\mathrm{hrs} \\ \mathrm{Rita}\text{'}\mathrm{s}1\mathrm{hour}\text{'}\mathrm{s}\mathrm{work}=\frac{1}{6} \\ \mathrm{Now},\left(\mathrm{Sam}+\mathrm{Rita}\right)\text{'}\mathrm{s}1\mathrm{hour}\text{'}\mathrm{s}\mathrm{work}=\frac{1}{4}+\frac{1}{6}=\frac{3+2}{12}=\frac{5}{12} \\ \mathrm{So},\mathrm{total}\mathrm{time}\mathrm{taken}\mathrm{by}\mathrm{Sam}\mathrm{and}\mathrm{Rita}\mathrm{to}\mathrm{pain}\mathrm{a}\mathrm{house}\mathrm{together}=\frac{12}{5}\mathrm{hrs}=\left(\frac{12}{5}\times 60\right)\min =144\min =2\mathrm{hrs}24\mathrm{minutes} \end{gathered}$$