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Ramon and Jason laid bricks for the six walls of a new building togeth

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Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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New post 05 May 2017, 04:40
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Question Stats:

63% (03:17) correct 38% (03:28) wrong based on 64 sessions

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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

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Re: Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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New post 12 May 2017, 13:10
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Bunuel 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


We are given that Ramon’s rate is 50% faster than Jason’s rate. If we let Jason’s rate = r, then Ramon’s rate = 1.5r. We are also given that the total time to complete the job was 84 hours, but Ramon worked 12 fewer hours than Jason did. If we let Jason’s time = t, then Ramon’s time = t - 12. Let’s now determine t:

t + t - 12 = 84

2t = 96

t = 48

So, Jason’s time was 48 hours and Ramon’s time was 36 hours.

Ramon’s work = 1.5r(36) = 54r

Jason’s work = 48r

Since total work = Ramon’s work + Jason’s work, and total work = 6 x 204 = 1224 bricks, we have:

1224 = 54r + 48r

1224 = 102r

12 = r

Thus, Ramon laid 1.5 x 12 = 18 bricks per hour.

Answer: C
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Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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New post Updated on: 05 May 2017, 10:29
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Given:

Time Taken by Jason = T hours
Time Taken by Ramon = T - 12 hours
Jason's Rate = 4R Bricks/Hour
Ramon's Rate = 6R Bricks/Hour

Total Time taken by Jason and Ramon = 84 hours

T+T-12 = 84
2T = 96
T = 48

Time Taken by Jason = 48 hours
Time Taken by Ramon = 48 - 12 = 36 hours

Total Work done by Ramon and Jason

4R*48 + 6R*36 = 6*204
192R+216R = 1224
408R=1224
R=3 bricks/hr

Ramon's Rate = 6 * 3 = 18 Bricks/hour

Answer is C. 18

Originally posted by quantumliner on 05 May 2017, 08:47.
Last edited by quantumliner on 05 May 2017, 10:29, edited 1 time in total.
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Re: Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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New post 05 May 2017, 08:50
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Let Ramon rate be R bricks/hour
Let Jason rate be J bricks/hour

Let time taken by Ramon be t. So time taken by Jason = t+12.

Ramon laid bricks at a rate fifty percent faster than did Jason. So R=1.5*J --> J = 2R/3

Total bricks = 6*204 = 1224

Total time taken = 84 hours ---> t+t+12 = 84 ---> 2t=72 ---> t=36

So, 1224 = R*t+J*(t+12) ---> 1224 = 36*R + (2R/3)*48 ---> 1224 = 36R+32R = 68R

R = 1224/68 = 18

Hence, C will be the answer.



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?
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Re: Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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New post 13 May 2017, 19:27
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Hi All,

Many Test Takers would use an algebraic approach to this question, which is fine. However, there are some interesting Number Property patterns that you can take advantage of - to minimize the amount of algebra that is required - and use estimation (and TESTing THE ANSWERS) to get to the solution.

To start, notice how all of the numbers in this prompt are even integers (6 walls, 204 bricks/wall, 84 total hours of work and all of the answers are even integers). This is important because we're told that Ramon lays bricks 50% FASTER than Jason does. From the answers, we know that Ramon's rate is an integer, but considering how 'nice' all of the other numbers are, it's really likely that Jason's rate is ALSO an integer. This allows us to eliminate 2 of the answers - B and D....

A: 24 is 50% greater than 16
B: 22 is 50% greater than 14.something
C: 18 is 50% greater than 12
D: 14 is 50% greater than 9.something
E: 12 is 50% greater than 8

Thus, the answer is almost certainly A, C or E.

The total number of bricks that need to be laid to complete the job is (6)(204) = 1224 bricks and we know that the pair worked a total of 84 hours... If we round both of those numbers off, we'd have 1200 bricks and 80 hours of work.

1200/80 = an average of 15 bricks/hour

Now, look at Answers A, C and E. Which is the ONLY one that gives us a potential average of 15 bricks/hour? Answer C (the average would be between 12 and 18). Answer A is too big and Answer E is too small.

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Re: Ramon and Jason laid bricks for the six walls of a new building togeth  [#permalink]

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Re: Ramon and Jason laid bricks for the six walls of a new building togeth   [#permalink] 08 Apr 2019, 19:54
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