If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

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If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

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Answer 1 · 2018-07-21T16:44:51

$2.4\ \text{hrs$

Explanation:

Sally alone can paint a house in $4\ text{hrs}$ Hence (fraction of) the work done by Sally in one hour

$=1/4$

Now, John alone can paint the house in $6\ text{hrs}$ Hence (fraction of) the work done by John in one hour

$=1/6$

If it takes $x\ \text{hrs}$ for Sally & John to paint the same house working together then the work done Sally & John in $x$ hrs will be (complete) $1$

$\therefore x(1/4+1/6)=1$

$x(5/12)=1$

$x=12/5$

$x=2.4$

Therefore it takes $2.4\ \text{hrs$ for Sally & John to paint the house together

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If Sally can paint a house in 4 hours, and John can paint the same house in 6 hour, how long will it take for both of them to paint the house together?

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