lheiannie07 wrote:Ramon and Jason laid bricks for the six walls of a new building together, each of them working alone at a constant rate. Ramon spent twelve fewer hours laying bricks than did Jason, but Ramon laid bricks at a rate fifty percent faster than did Jason. If each wall required 204 bricks, and the total time it took the two men to complete the job was 84 hours, how many bricks per hour did Ramon lay?
A. 24
B. 22
C. 18
D. 14
E. 12
Total number of bricks = (number of walls) (bricks per wall) = (6)(204) = 1224.
Let J = Jason's time.
Since Ramon works for 12 fewer hours, Ramon's time = J-12.
Since the total time is 84 hours, we get:
J + (J-12) = 84
2J = 96
J = 48.
Thus:
Jason's time = 48 hours.
Ramon's time = 48-12 = 36 hours.
Since Ramon's rate is 50% faster than Jason's rate, Ramon's rate is 150% = 3/2 of Jason's rate.
Since Ramon's rate is 3/2 of Jason's rate, Jason's rate is 2/3 of Ramon's rate.
Let R = Ramon's rate, implying that Jason's rate = (2/3)R.
Since Ramon works for 36 hours, Ramon's output = rt = R*36 = 36R.
Since Jason works for 48 hours, Jason's output = rt = (2/3)(R) * 48 = 32R.
Since the total output is 1224 bricks, we get:
36R + 32R = 1224
68R = 1224
R = 18 bricks per hour.
The correct answer is
C.
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