Question 1031410
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If Yathu was to paint a house by himself, he would take 6 hour. If Mazhahir was to paint a house by himself, 
he would tack it 10 hours. How long did both of them take to paint the house together
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Since Yathu can paint a living room in 6 hours, he paints {{{1/6}}} of the living room area in one hour. It is his rate.

The Mazhahir paints {{{1/10}}} of the living room area in one hour.

If the two painters work together, they paint {{{1/6 + 1/10}}} = {{{5/30 + 3/30}}} = {{{8/30}}} = {{{4/15}}} of the room area per hour. 
(When the painters work together, their rates add up.)

Hence, they need {{{15/4}}} = {{{3}}}{{{3/4}}} hour = 3 hours and 45 minutes to complete the job, if they work together.


It is a typical problem on joint work.

For a variety of similar solved joint-work problems see the lesson 
<A HREF=https://www.algebra.com/algebra/homework/Rate-of-work-word-problems/Word-problems-WORKING-TOGETHER-by-Fractions.lesson>Using fractions to solve word problems on joint work</A> in this site, 
and also associated lessons.
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