Blog: Harry can paint a room in 55 minutes. Sal can paint the same room in 66 minutes. How long would it take them to paint the same room if they work...

Saturday, October 17, 2015

The amount of work Harry can do in one minute = $\displaystyle\frac{{1}}{{55}}$

(in 55 minutes he can paint 1 room , then in one minute 1/55 of room)

The amount of work Sal can do in one minute = $\displaystyle\frac{{1}}{{66}}$

(66 minutes he can paint 1 room, then in one minute 1/66 of room)

The amount of work together they do in one minute= $\displaystyle{\left(\frac{{1}}{{55}}+\frac{{1}}{{66}}\right)}$

Time taken to paint the same room by them = $\displaystyle\frac{{1}}{{\frac{{1}}{{55}}+\frac{{1}}{{66}}}}$

(in one minute (1/55 + 1/66) of work, then in x minutes the entire room. by cross-multiplication we get x value)

$\displaystyle=\frac{{{55.66}}}{{{55}+{66}}}=\frac{{3630}}{{121}}={30}$ minutes

Together they take 30 minutes to paint the same room.

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