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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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New post 11 Apr 2017, 00:04
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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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New post 11 Apr 2017, 05:34
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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]

Answer:

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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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New post 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

\(T =\) \(\frac{8t}{3}\)

Answer should be.
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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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New post 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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If x laborers can build a wall in t hours, then in terms of t how long  [#permalink]

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New post 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
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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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New post 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

Answer: C
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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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New post 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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