Two bricklayers, Alan and David, each place 30 bricks per hour. Alan worked three times as many hours as David, and the two of them placed a total of 600 bricks. How many bricks did David lay?
I need to find the number of bricks that David laid, so I'll call that x. Then the number of bricks that Alan laid must be 600 - x, since they placed 600 bricks together. I also know that Alan worked three times as many hours as David, so if I let y be the number of hours that David worked, then Alan worked 3y hours. Now I can use the rate equation for each bricklayer: bricks = rate times hours. For Alan, this means 600 - x = 30 times 3y, or 600 - x = 90y. For David, this means x = 30 times y, or x = 30y. I can substitute x = 30y into the first equation and get 600 - 30y = 90y. Adding 30y to both sides, I get 600 = 120y. Dividing both sides by 120, I get y = 5. This means that David worked 5 hours, and Alan worked 3 times 5, or 15 hours. To find the number of bricks that David laid, I can plug y = 5 into x = 30y and get x = 30 times 5, or x = 150. So David laid 150 bricks.

