Question

1. A machine fills containers at a rate of 135 containers per minute.how long would it take to fill 1000 containers at the same rate?
2. Nozi cycles for 2 hours and 20 minutes at a constant speed of 18km/h.how far does she go?

Answer 1

$\displaystyle(1)\\ \begin{aligned} 135 \hspace{0.1cm} \textsf{containers}\hspace{0.1cm} &=1\hspace{0.1cm}\textsf{minute}\\ 1 \hspace{0.1cm} \textsf{container}\hspace{0.1cm} &=\frac{1}{135}\hspace{0.1cm}\textsf{minute}\\ 1000\hspace{0.1cm} \textsf{containers}\hspace{0.1cm} &= \frac{1000}{135}\hspace{0.1cm}\textsf{minutes} \\&= \frac{200}{27}\hspace{0.1cm}\textsf{minutes} \\&\approx 7.41\hspace{0.1cm}\textsf{minutes} \end{aligned}\\ (2)\\ t = 2\hspace{0.1cm}\textsf{hr}\hspace{0.1cm}20\hspace{0.1cm}\textsf{mins} \\ \begin{aligned} t &= 2 + \frac{20}{60}\\ t &= 2 + \frac{1}{3} &= \frac{7}{3}\hspace{0.1cm} \textsf{hrs} \end{aligned}\\ \textsf{Speed} = \frac{\textsf{distance}}{\textsf{time}}\\ \textsf{distance} = \textsf{Speed} \times \textsf{time}\\ \textsf{distance} = \frac{7}{3} \times 18 = 42 \hspace{0.1cm} \textsf{km}$