[tex]\text{The boy can mow the lawn in 30 minutes,}\\ \text{so in 1 minute he can mow the lawn}=\frac{1}{30}\text{ part}\\ \\ \text{And his sister can mow the lawn in 45 minutes,}\\ \text{so in 1 minute she can mow}=\frac{1}{45} \text{ part}\\ \\ \text{so if they work together, in 1 minute they can mow}\\ \\ =\frac{1}{30}+\frac{1}{45}[/tex]
[tex]=\frac{3+2}{90}\\ \\ =\frac{5}{90}\\ \\ =\frac{1}{18}\\ \\ \text{since in 1 mintute together they can mow}=\frac{1}{18}\text{ part},\\ \\ \text{so they together will mow the lawn in}=18 \text{ minutes}[/tex]
Hence they together will mow the lawn in 18 minutes
