Convert foot / (minute • second) to mile / square minute
Learn how to convert
1
foot / (minute • second) to
mile / square minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{foot}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{foot}{minute \times second}\right) = {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{mile}{square \text{ } minute}\right) = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{foot}{minute \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{mile}{square \text{ } minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{0.3048}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{1609.344}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{0.3048}{2.16 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times 10^{3}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{0.3048}{2.16 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{5}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6 \times {\color{rgb(255,204,153)} \cancel{10^{3}}}}\)
\(\text{Simplify}\)
\(\dfrac{0.3048}{2.16 \times 10^{2}} = {\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6} = \dfrac{0.3048}{2.16 \times 10^{2}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6}{1609.344}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{1609.344}{3.6} \times \dfrac{3.6}{1609.344} = \dfrac{0.3048}{2.16 \times 10^{2}} \times \dfrac{3.6}{1609.344}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{1609.344}} \times {\color{rgb(99,194,222)} \cancel{3.6}}}{{\color{rgb(99,194,222)} \cancel{3.6}} \times {\color{rgb(255,204,153)} \cancel{1609.344}}} = \dfrac{0.3048 \times 3.6}{2.16 \times 10^{2} \times 1609.344}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{0.3048 \times 3.6}{2.16 \times 10^{2} \times 1609.344}\)
Rewrite equation
\(\dfrac{1.0}{10^{2}}\text{ can be rewritten to }10^{-2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-2} \times 0.3048 \times 3.6}{2.16 \times 1609.344}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx0.0000031566\approx3.1566 \times 10^{-6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{foot}{minute \times second}\right)\approx{\color{rgb(20,165,174)} 3.1566 \times 10^{-6}}\left(\dfrac{mile}{square \text{ } minute}\right)\)
