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

x labourers can built 8 wallin in 8t hours,,,

3 times labouresr can build in 8t/3 hours

ans 8t/3

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

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

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

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

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

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

\(\frac{?}{t} = \frac{8}{3}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = \frac{{8t}}{3}\)

The above follows the notations and rationale taught in the GMATH method.

rate per worker ; 1/t and for 3 times worker 3/t
so for 8 walls time will be w= r*t
t= 8t/3
IMO C

X laborers take t hours to build a wall
3x laborers will take t/3 hours to build a wall
3x laborers will ale 8t/3 hours to build 8 walls

IMO C

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