Convert mile / (hour • minute) to inch / square hour
Learn how to convert
1
mile / (hour • minute) to
inch / square hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mile}{hour \times minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mile}{hour \times minute}\right) = {\color{rgb(89,182,91)} \dfrac{1609.344}{2.16 \times 10^{5}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1609.344}{2.16 \times 10^{5}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{inch}{square \text{ } hour}\right) = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mile}{hour \times minute}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{inch}{square \text{ } hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{2.16 \times 10^{5}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1609.344}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{2.16 \times 10^{5}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1609.344}{2.16 \times 10^{5}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{7}}\)
Cancel factors on both sides
\(\text{Cancel factors}\)
\(\dfrac{1609.344}{2.16 \times {\color{rgb(255,204,153)} \cancel{10^{5}}}} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times {\color{rgb(255,204,153)} \cancelto{10^{2}}{10^{7}}}}\)
\(\text{Simplify}\)
\(\dfrac{1609.344}{2.16} = {\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{2}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{2}} = \dfrac{1609.344}{2.16}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{1.296 \times 10^{2}}{2.54 \times 10^{-2}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{2.54 \times 10^{-2}}{1.296 \times 10^{2}} \times \dfrac{1.296 \times 10^{2}}{2.54 \times 10^{-2}} = \dfrac{1609.344}{2.16} \times \dfrac{1.296 \times 10^{2}}{2.54 \times 10^{-2}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}} \times {\color{rgb(166,218,227)} \cancel{1.296}} \times {\color{rgb(76,153,0)} \cancel{10^{2}}}}{{\color{rgb(166,218,227)} \cancel{1.296}} \times {\color{rgb(76,153,0)} \cancel{10^{2}}} \times {\color{rgb(255,204,153)} \cancel{2.54}} \times {\color{rgb(99,194,222)} \cancel{10^{-2}}}} = \dfrac{1609.344 \times 1.296 \times 10^{2}}{2.16 \times 2.54 \times 10^{-2}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 1.296 \times 10^{2}}{2.16 \times 2.54 \times 10^{-2}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-2}}\text{ can be rewritten to }10^{2}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{2} \times 1609.344 \times 1.296 \times 10^{2}}{2.16 \times 2.54}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 1609.344 \times 1.296}{2.16 \times 2.54}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 3801600 = 3.8016 \times 10^{6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mile}{hour \times minute}\right) = {\color{rgb(20,165,174)} 3.8016 \times 10^{6}}\left(\dfrac{inch}{square \text{ } hour}\right)\)
