The bricklayers

small_unicorn

A contractor estimated that one of his two bricklayers would take 9 hours to build a certain wall and the other 10 hours. However, he knew from experience that when they worked together, 10 fewer bricks got laid per hour. Since he was in hurry, he put both men on the job and found it took exactly 5 hours to build the wall.
How many bricks did it contain ?

**Posted:** Sun Nov 08, 2009 4:24 pm

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Juggle

2008-2009 MOEMS ED = 18; Purple Comet Alone = 8

Dojo

The first bricklayer gets $\dfrac{1}{9}$ of the job done in an hour, and the second gets $\dfrac{1}{10}$ of the job done in an hour. Technically, the two get $\dfrac{1}{9}+\dfrac{1}{10}=\dfrac{19}{90}$ done per hour, but they actually get 10 less bricks per hour. The pair should have gotten $\dfrac{95}{90}$ of the job done, which is $\dfrac{1}{18}$ extra on the job. This means that $\dfrac{1}{18}$ of the job is $5\times 10=50$ bricks. There are a total of $900$ bricks to be layed.

**Posted:** Sun Nov 08, 2009 10:04 pm

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-Dojo Smile

vgandikota · New Member Offline Joined: 08 Oct 2009 Posts: 4

Great Problem

**Posted:** Tue Nov 10, 2009 4:34 pm