Answer: The required equation is [tex]\frac{1}{t}=\frac{1}{20}+\frac{1}{30}[/tex].
They will take 1.2 hour to install the fountain in school if they wirk together.
Step-by-step explanation:
Given: The time taken by Casey to install a fountain in a school= 20 hours
The time taken by Samuel to install the same fountain in school= 30 hours
Let t be the time of installation of fountain if they work together, then we have the following equation:-
[tex]\frac{1}{t}=\frac{1}{20}+\frac{1}{30}\\\\\Rightarrow\frac{1}{t}=\frac{30+20}{20\times30}\\\\\Rightarrow\ \frac{1}{t}=\frac{50}{60}\\\\\Rightarrow\ t=\frac{60}{50}\\\\\Rightarrow\ t=1.2[/tex]
Hence, they will take 1.2 hour to install the fountain in school if they wirk together.
Answer: The answer is 1.2 hours.
Step-by-step explanation: Given that Casey and Samuel can install a fountain separately in 20 hours and 3 hours respectively. Working together, they take 't' hours to install the fountain.
In 1 hours the part of the fountain that Casey install = [tex]\dfrac{1}{20}.[/tex]
In 1 hour, the part of the fountain that Samuel install = [tex]\dfrac{1}{30}.[/tex]
Together, in 1 hour, they will install [tex](\dfrac{1}{20}+\dfrac{1}{30})[/tex] part of the fountain.
Also, it is given that they take 't' hours together to install the fountain, so in 1 hour, they will install [tex]\dfrac{1}{t}[/tex] part of the fountain.
Therefore, we can write
[tex]\dfrac{1}{t}=\dfrac{1}{20}+\dfrac{1}{30},[/tex] which is the expression for 't'.
Solving this equation, we get
[tex]\dfrac{1}{t}=\dfrac{30+20}{60}\\\\\Rightarrow\dfrac{1}{t}=\dfrac{50}{60}\\\\\Rightarrow t=\dfrac{6}{5}=1.2.[/tex]
Thus, they both complete installing the fountain in 1.2 hours while working together.
