Hayley Bernard

2022-07-25

If one person can clean a house in 5 hours and second person can clean the same house in 4 hours, how long will it take to clean the house if they work together?
a) 9 hours
b) 4.5 hours
c) 22/9 hours
d) 1 hour

umshikepl

Expert

Step 1
Given that one person can clean the house in 5 hours and second person can clean in 4 hours.
House clean by one person in one hours $=\frac{1}{5}$ unit
house clean by second person in one hour $=\frac{1}{4}$ unit
when they work together
Then house clean by both in one hour $=\left(\frac{1}{5}+\frac{1}{4}\right)$ unit
$=\frac{9}{20}unit$
Step 2
Since $=\frac{9}{20}unit$ cleaning is completed by both in one hours
hence 1 unit cleaning is completed by both in $\frac{1}{\left(\frac{9}{20}\right)}$ hours
$=\frac{20}{9}$ hours
$=2\frac{2}{9}$ hours
Thus total time taken is $=2\frac{2}{9}$ hours.
Option (c) is correct.

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