SOLUTION: 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 tog

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Question 561355: 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 a 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?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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 a 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?
:
let b = no. of bricks in the wall
then
b%2F9 = no. of bricks laid per hr by the 1st bricklayer
and
b%2F10 = no. of brick laid per hr by the 2nd bricklayer
:
In 5 hrs, 50 less bricks were laid when they worked together
:
b = 5*b%2F10 + 5*b%2F9 - 50
b = %285b%29%2F10 + %285b%29%2F9 - 50
multiply by 90 to get rid of the denominators
90b = 9(5b) + 10(5b) - 90(50)
90b = 45b + 50b - 4500
90b = 95b - 4500
4500 = 95b - 90b
4500 = 5b
b = 4500/5
b = 900 bricks in the wall
:
:
See if that checks out:
900/9 = 100 per hr
900/10 = 90 per hr
5(100) + 5(90) = 950 bricks, but they lay 5(10) less if working together, hence 900 bricks