Question

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 1

Answer:

Therefore the wall contained 900 bricks.

Step-by-step explanation:

Given that there are two bricklayers.

In 9 hours, the first bricklayers built a certain wall and other bricklayer takes 10 hours to build the wall.

Let b = the number of bricks of the wall.

The number brick laid in 9 hour by first bricklayer is b

Then the number brick laid in 1 hour by first bricklayer is $\frac{b}{9}$.

The number brick laid in 5 hour by first bricklayer is $\frac{5b}{9}$.

The number brick laid in 10 hour by second bricklayer is b

Then the number brick laid in 1 hour by second bricklayer is $\frac{b}{10}$

Then the number brick laid in 5 hour by second bricklayer is $\frac{5b}{10}$

Again given that, if they worked together 10 fewer bricks got laid per hour.

If they worked together for 5 hours,then (5×10)=50 less bricks were laid by them.

The number of brick were laid by them is $=\frac{5b}{9}+\frac{5b}{10}-50$.

But the wall made by b number of bricks.

According to the problem,

$\frac{5b}{9}+\frac{5b}{10}-50=b$

$\Rightarrow \frac{50b+45b-4500}{90}=b$     [ The L.C.M of 9 and 10 is =10]

$\Rightarrow{50b+45b-4500=90b$

$\Rightarrow 95b-4500=90b$

$\Rightarrow 95b-90b=4500$

$\Rightarrow 5b=4500$

$\Rightarrow b=\frac{4500}{5}$

$\Rightarrow b=900$

Therefore the wall contained 900 bricks.