# Convert mile / (hour • second) to foot / (minute • second)

Learn how to convert 1 mile / (hour • second) to foot / (minute • second) step by step.

## Calculation Breakdown

Set up the equation
$$1.0\left(\dfrac{mile}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{minute \times second}\right)$$
Define the base values of the selected units in relation to the SI unit $$\left(\dfrac{meter}{square \text{ } second}\right)$$
$$\text{Left side: 1.0 } \left(\dfrac{mile}{hour \times second}\right) = {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Right side: 1.0 } \left(\dfrac{foot}{minute \times second}\right) = {\color{rgb(125,164,120)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}$$
Insert known values into the conversion equation to determine $${\color{rgb(20,165,174)} x}$$
$$1.0\left(\dfrac{mile}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{foot}{minute \times second}\right)$$
$$\text{Insert known values } =>$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{0.3048}{2.16 \times 10^{5}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}$$
$$\text{Or}$$
$$1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{0.3048}{2.16 \times 10^{5}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}$$
$$\text{Cancel SI units}$$
$$1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{0.3048}{2.16 \times 10^{5}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}$$
$$\text{Conversion Equation}$$
$$\dfrac{1609.344}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{2.16 \times 10^{5}}$$
Cancel factors on both sides
$$\text{Cancel factors}$$
$$\dfrac{1609.344}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{2.16 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}}$$
$$\text{Simplify}$$
$$\dfrac{1609.344}{3.6} = {\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{2.16 \times 10^{2}}$$
Switch sides
$${\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{2.16 \times 10^{2}} = \dfrac{1609.344}{3.6}$$
Isolate $${\color{rgb(20,165,174)} x}$$
Multiply both sides by $$\left(\dfrac{2.16 \times 10^{2}}{0.3048}\right)$$
$${\color{rgb(20,165,174)} x} \times \dfrac{0.3048}{2.16 \times 10^{2}} \times \dfrac{2.16 \times 10^{2}}{0.3048} = \dfrac{1609.344}{3.6} \times \dfrac{2.16 \times 10^{2}}{0.3048}$$
$$\text{Cancel}$$
$${\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{0.3048}} \times {\color{rgb(99,194,222)} \cancel{2.16}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{2.16}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{0.3048}}} = \dfrac{1609.344 \times 2.16 \times 10^{2}}{3.6 \times 0.3048}$$
$$\text{Simplify}$$
$${\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 2.16 \times 10^{2}}{3.6 \times 0.3048}$$
Solve $${\color{rgb(20,165,174)} x}$$
$${\color{rgb(20,165,174)} x} = 316800 = 3.168 \times 10^{5}$$
$$\text{Conversion Equation}$$
$$1.0\left(\dfrac{mile}{hour \times second}\right) = {\color{rgb(20,165,174)} 3.168 \times 10^{5}}\left(\dfrac{foot}{minute \times second}\right)$$