Question

A contractor estimated that one of his two brick layers 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 were 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 the wall contain?

Answer 1

Answer:

900

Step-by-step explanation:

Assume x brick

X*(1／9+1/10）一 10=X/5

X(19/90-1/5)=10

X*(1/90)=10

X=900

Answer 2

To solve this question:

• We find how many bricks each produce per hour.
• Then, we expand this to consider five hours.
• Relating to the amount of bricks built, and the fact that with them together, 10 fewer bricks are laid per hour, we build an equation, and solve for b, the total amount of bricks.

Doing this, we get that the wall contained 900 bricks.

Layers:

• One takes 9 hours, so in one hour, he produces: $\frac{b}{9}$ bricks;
• One takes 10 hours, so in one hour, he produces: $\frac{b}{10}$ bricks.
• For each hour, with them together, 10 fewer layers are produced.

Five hours:

Considering that they will work five hours, we have that:

• The first layer produces $\frac{5b}{9}$ bricks.
• The second produces $\frac{5b}{10}$ bricks.
• 10 fewer per hour, so in 5 hours, 5*10 = 50 fewer.
• Total of b bricks in the wall.

With this, the equation is:

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

The least common multiple of 9 and 10 is 90, thus:

$b = \frac{50b + 45b - 4500}{90}$

$90b = 95b - 4500$

$5b = 4500$

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

$b = 900$

Thus, the wall contained 900 bricks.

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