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# If x laborers can build a wall in t hours, then in terms of t how long

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If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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11 Apr 2017, 00:04
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Question Stats:

76% (01:30) correct 24% (01:34) wrong based on 110 sessions

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If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

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Re: If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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11 Apr 2017, 05:34
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Top Contributor
Bunuel wrote:
If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

Given: x laborers can build ONE wall in t hours
This means x laborers can build EIGHT walls in 8t hours
So, 3x laborers can build EIGHT walls in 8t/3 hours [if we triple the number of laborers, then their combined rate is tripled, which means the completion time is reduced to 1/3 the original time]

Cheers,
Brent
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If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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11 Apr 2017, 06:40
Bunuel wrote:
If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

Solution with RT = W formula approach.

Given time = $$t$$ and work $$= 1$$ (wall)

$$xR * t$$ $$= 1$$

hence $$R$$ = $$\frac{1}{xt}$$

now the number of labors are 3x and work is 8 and time taken T is asked.

$$RT = W$$

$$3xR * T = 8$$

$$3x$$ * $$\frac{1}{xt}$$ $$* T = 8$$

$$\frac{3T}{t}$$ = 8

$$T =$$ $$\frac{8t}{3}$$

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Re: If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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11 Apr 2017, 09:28
x labourers can built 8 wallin in 8t hours,,,

3 times labouresr can build in 8t/3 hours

ans 8t/3
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Joined: 07 Dec 2014
Posts: 1152
If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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11 Apr 2017, 10:12
Bunuel wrote:
If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

rate of 1 worker=1/xt
rate of 3x workers=3x/xt=3/t
8/(3/t)=8t/3=time for 3x workers to build 8 walls
C
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Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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18 Apr 2017, 15:23
1
Bunuel wrote:
If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

We are given that x laborers can build a wall in t hours. Thus, the rate of the x laborers is 1/t and the rate for 3 times the number of laborers is 3/t. We need to determine how long it will take 3 times the number of laborers to build 8 walls. Thus:

time = work/rate

time = 8/(3/t) = 8t/3

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Re: If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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26 Aug 2018, 12:21
Bunuel wrote:
If x laborers can build a wall in t hours, then in terms of t how long would it take 3 times the number of laborers to build eight walls?

A. t/24
B. 3t/8
C. 8t/3
D. 8t
E. 24t

$$?\,\, = \,\,f\left( t \right)\,\,\,\,\,\,\,\,\left[ {\text{h}} \right]$$

$$\begin{array}{*{20}{c}} {x\,\,{\text{people}}} \\ {3x\,\,{\text{people}}} \end{array}\,\,\,\,\,\,\begin{array}{*{20}{c}} {t\,\,{\text{h}}} \\ {?\,\,{\text{h}}} \end{array}\,\,\,\,\,\,\,\begin{array}{*{20}{c}} {1\,\,{\text{job}}} \\ {8\,{\text{job}}} \end{array}$$

$$\begin{array}{*{20}{c}} {} \\ {\left( { \cdot \,3} \right)} \\ {} \end{array}\,\,\,\,\begin{array}{*{20}{c}} {x\,\,{\text{people}}} \\ {3x\,\,{\text{people}}} \\ {3x\,\,{\text{people}}} \end{array}\,\,\,\,\,\,\,\begin{array}{*{20}{c}} {t\,\,{\text{h}}} \\ {t\,\,{\text{h}}} \\ {?\,\,{\text{h}}} \end{array}\,\,\,\,\,\,\,\begin{array}{*{20}{c}} {1\,\,{\text{job}}} \\ {3\,\,{\text{jobs}}} \\ {8\,\,{\text{jobs}}} \end{array}$$

$$\left( {3x\,\,{\text{people}}} \right)\,\,\,\,\,\, \downarrow \begin{array}{*{20}{c}} {t\,\,{\text{h}}} \\ {?\,\,{\text{h}}} \end{array}\,\,\,\,\,\, \downarrow \begin{array}{*{20}{c}} {3\,\,{\text{jobs}}} \\ {8\,\,{\text{jobs}}} \end{array}$$

$$\frac{?}{t} = \frac{8}{3}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{8t}}{3}$$

The above follows the notations and rationale taught in the GMATH method.
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Re: If x laborers can build a wall in t hours, then in terms of t how long &nbs [#permalink] 26 Aug 2018, 12:21
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