Question

Paul can install a 300-square-foot hardwood floor in 18 hours. Matt can install the same floor in 22 hours. How long would it take Paul and Matt to install the floor working together?A. 4 hoursB. 9.9 hoursC. 13.2 hoursD. 30 hours

Answer 1

Answer: B. 9.9 hours

Step-by-step explanation:

Given : Paul can install a 300-square-foot hardwood floor in 18 hours.

We consider whole job as 1.

Rate of work per hour for Paul = $r_1=\dfrac{1}{18}$

Matt can install the same floor in 22 hours.

Rate of work per hour for Matt = $r_2=\dfrac{1}{22}$

Now , when they both work together , the rate of work = $r=\dfrac{1}{t}$ , where t is time taken by both together.

Since , $r=r_1+r_2$

$\dfrac{1}{t}=\dfrac{1}{18}+\dfrac{1}{22}$

$\dfrac{1}{t}=\dfrac{11+9}{198}=\dfrac{20}{198}=\dfrac{10}{99}\\\\\Rightarrow\ t=\dfrac{99}{10}=9.9$

Hence, it would take 9.9 hours to install the floor working together.

Therefore , the correct answer is  B. 9.9 hours .