Question

The first team of workers received $50kg$ of cement less than the second team. For every hour of work, the first team was using $150kg$ of cement, while the second team was using $200kg$.In three hours the first team had $1.5$ times as much remaining cement as the second team. How much cement was delivered to each team of workers?

Answer 1

Step-1: Forming equations in $x$ and $y$:

Let, the amount of cement received by the first team be $x$ and the cement received by the second team be $y$.

It is given that, the first team received $50\mathrm{Kg}$ of cement less than the second team.

Therefore,

$x=y-50...\left(\mathrm{i}\right)$

For every hour of work, the first team use $150\mathrm{Kg}$ of cement, while the second team use $200\mathrm{Kg}$

Cement used by first team after three hours is $150\times 3=450$

Cement used by second team after three hours is $200\times 3=600$

After three hours;

The amount first team had leftover was $x-450$

The amount second team had leftover was $y-600$

After three hours the first team had $1.5$ times as much remaining cement as the second team.

$\begin{array}{rcl}1.5\times (y-600)& =& x-450\\ 1.5y-900& =& x-450\\ 1.5y-x& =& 450...\left(\mathrm{ii}\right)\end{array}$

Step-2: Solve equations for $x$ and $y$:

Add equation $\left(\mathrm{i}\right)$ and $\left(\mathrm{ii}\right)$:

$\begin{array}{rcl}1.5y-x+x& =& 450+y-50\\ \Rightarrow 0.5y& =& 400\\ \Rightarrow y& =& 800\end{array}$

Substitute $y=800$ in $x=y-50$:

$$\begin{gathered} x=y-50 \\ \Rightarrow x=800-50 \\ \Rightarrow x=750 \end{gathered}$$

Hence, the first team received $750kg$ and the second team received $800kg$ of cement.