Question

a bricklayers assistant starts building a wall laying 50 bricks per hour. Two hours later the master bricklayer joins the assistant and both lay bricks. The master bricklayer lays 80 bricks per hour. write an equation stating that the assistant and the master have laid the same number of bricks. how long has each one worked when they have laid the same number? ​

Answer 1

• 80t = 50(t+2)
• master: 3 1/3 hours
• assistant: 5 1/3 hours

Explanation:

Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.

Rate and output

The output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).

Here is the equation that says their output is the same:

80t = 50(t+2)

Time

Solving the equation for t, we have ...

80t = 50t +100

30t = 100 . . . . . . . . . subtract 50t

t = 3 1/3 . . . . . . . divide by 30

The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.

The assistant bricklayer has worked 5 1/3 hours at that time.

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Additional comment

Each will have laid (80)(3 1/3) = 266 2/3 bricks.