Convert mile / second to yard / hour
Learn how to convert
1
mile / second to
yard / hour
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mile}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{yard}{hour}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mile}{second}\right) = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{meter}{second}\right)} = {\color{rgb(89,182,91)} 1609.344\left(\dfrac{m}{s}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{yard}{hour}\right) = {\color{rgb(125,164,120)} \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}\left(\dfrac{meter}{second}\right)} = {\color{rgb(125,164,120)} \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}\left(\dfrac{m}{s}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mile}{second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{yard}{hour}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} 1609.344} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s}\right)}}\)
\(\text{Conversion Equation}\)
\(1609.344 = {\color{rgb(20,165,174)} x} \times \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}} = 1609.344\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{3.6 \times 10^{3}}{9.144 \times 10^{-1}}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{9.144 \times 10^{-1}}{3.6 \times 10^{3}} \times \dfrac{3.6 \times 10^{3}}{9.144 \times 10^{-1}} = 1609.344 \times \dfrac{3.6 \times 10^{3}}{9.144 \times 10^{-1}}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{9.144}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}} \times {\color{rgb(166,218,227)} \cancel{3.6}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}}}{{\color{rgb(166,218,227)} \cancel{3.6}} \times {\color{rgb(76,153,0)} \cancel{10^{3}}} \times {\color{rgb(255,204,153)} \cancel{9.144}} \times {\color{rgb(99,194,222)} \cancel{10^{-1}}}} = 1609.344 \times \dfrac{3.6 \times 10^{3}}{9.144 \times 10^{-1}}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 3.6 \times 10^{3}}{9.144 \times 10^{-1}}\)
Rewrite equation
\(\dfrac{1.0}{10^{-1}}\text{ can be rewritten to }10\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10.0 \times 1609.344 \times 3.6 \times 10^{3}}{9.144}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{4} \times 1609.344 \times 3.6}{9.144}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x} = 6336000 = 6.336 \times 10^{6}\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mile}{second}\right) = {\color{rgb(20,165,174)} 6.336 \times 10^{6}}\left(\dfrac{yard}{hour}\right)\)
