Question

Company X can install chairs in a theater in 10 hours company Y can install them in 15 hours. How long would the two companies working together need to install the chairs?

Answer 1

Answer: 6 hours

Step-by-step explanation:

Given : The time taken by Company X to install chairs : $t_1=10\text{ hours}$

The time taken by Company Y to install chairs : $t_2=15\text{ hours}$

Then , the time taken (T) by both of them to install the chairs if they work together is given by :-

$\dfrac{1}{T}=\dfrac{1}{t_1}+\dfrac{1}{t_2}\\\\\Rightarrow\ \dfrac{1}{T}=\dfrac{1}{10}+\dfrac{1}{15}\\\\\Rightarrow\dfrac{1}{T}=\dfrac{10}{60}\\\\\Rightarrow\ T=6$

Hence, it will take 6 hours to the two companies if they working together .