Convert foot / (hour • second) to mile / (hour • minute)
Learn how to convert
1
foot / (hour • second) to
mile / (hour • minute)
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{foot}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{hour \times minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{foot}{hour \times second}\right) = {\color{rgb(89,182,91)} \dfrac{0.3048}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{0.3048}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mile}{hour \times minute}\right) = {\color{rgb(125,164,120)} \dfrac{1609.344}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1609.344}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{foot}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{hour \times minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1609.344}{2.16 \times 10^{5}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.3048}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1609.344}{2.16 \times 10^{5}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1609.344}{2.16 \times 10^{5}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{0.3048}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{2.16 \times 10^{5}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{0.3048}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{2.16 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}}\)
\(\text{Simplify}\)
\(\dfrac{0.3048}{3.6} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{2.16 \times 10^{2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{2.16 \times 10^{2}} = \dfrac{0.3048}{3.6}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{2.16 \times 10^{2}}{1609.344}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{2.16 \times 10^{2}} \times \dfrac{2.16 \times 10^{2}}{1609.344} = \dfrac{0.3048}{3.6} \times \dfrac{2.16 \times 10^{2}}{1609.344}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1609.344}} \times {\color{rgb(99,194,222)} \cancel{2.16}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}}}{{\color{rgb(99,194,222)} \cancel{2.16}} \times {\color{rgb(166,218,227)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{1609.344}}} = \dfrac{0.3048 \times 2.16 \times 10^{2}}{3.6 \times 1609.344}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.3048 \times 2.16 \times 10^{2}}{3.6 \times 1609.344}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0113636364\approx1.1364 \times 10^{-2}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{foot}{hour \times second}\right)\approx{\color{rgb(20,165,174)} 1.1364 \times 10^{-2}}\left(\dfrac{mile}{hour \times minute}\right)\)
