Solve {l}{3*0.6=1/2*10t}{3*0.8+10.5t=Vt}

$$\left. \begin{array} { l } { 3 \times 0.6 = \frac { 1 } { 2 } \times 10 t } \\ { 3 \times 0.8 + 10.5 t = V t } \end{array} \right.$$

Solve for t, V

$$t=0.36$$

$$V = \frac{103}{6} = 17\frac{1}{6} \approx 17.166666667$$

Solution Steps

Consider the first equation. Multiply 3 and 0.6 to get 1.8.

$$1.8=\frac{1}{2}\times 10t$$

Multiply \frac{1}{2} and 10 to get 5.

$$1.8=5t$$

Swap sides so that all variable terms are on the left hand side.

$$5t=1.8$$

Divide both sides by 5.

$$t=\frac{1.8}{5}$$

Expand \frac{1.8}{5} by multiplying both numerator and the denominator by 10.

$$t=\frac{18}{50}$$

Reduce the fraction \frac{18}{50} to lowest terms by extracting and canceling out 2.

$$t=\frac{9}{25}$$

Consider the second equation. Insert the known values of variables into the equation.

$$3\times 0.8+10.5\times \frac{9}{25}=V\times \frac{9}{25}$$

Multiply 3 and 0.8 to get 2.4.

$$2.4+10.5\times \frac{9}{25}=V\times \frac{9}{25}$$

Multiply 10.5 and \frac{9}{25} to get \frac{189}{50}.

$$2.4+\frac{189}{50}=V\times \frac{9}{25}$$

Add 2.4 and \frac{189}{50} to get \frac{309}{50}.

$$\frac{309}{50}=V\times \frac{9}{25}$$

Swap sides so that all variable terms are on the left hand side.

$$V\times \frac{9}{25}=\frac{309}{50}$$

Multiply both sides by \frac{25}{9}, the reciprocal of \frac{9}{25}.

$$V=\frac{309}{50}\times \frac{25}{9}$$

Multiply \frac{309}{50} and \frac{25}{9} to get \frac{103}{6}.

$$V=\frac{103}{6}$$

The system is now solved.

$$t=\frac{9}{25} V=\frac{103}{6}$$