Convert mile / (hour • second) to knot / minute
Learn how to convert
1
mile / (hour • second) to
knot / minute
step by step.
Calculation Breakdown
Set up the equation
\(1.0\left(\dfrac{mile}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{knot}{minute}\right)\)
Define the base values of the selected units in relation to the SI unit \(\left(\dfrac{meter}{square \text{ } second}\right)\)
\(\text{Left side: 1.0 } \left(\dfrac{mile}{hour \times second}\right) = {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}\left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Right side: 1.0 } \left(\dfrac{knot}{minute}\right) = {\color{rgb(125,164,120)} \dfrac{50.93}{5940.0}\left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(125,164,120)} \dfrac{50.93}{5940.0}\left(\dfrac{m}{s^{2}}\right)}\)
Insert known values into the conversion equation to determine \({\color{rgb(20,165,174)} x}\)
\(1.0\left(\dfrac{mile}{hour \times second}\right)={\color{rgb(20,165,174)} x}\left(\dfrac{knot}{minute}\right)\)
\(\text{Insert known values } =>\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \times {\color{rgb(89,182,91)} \left(\dfrac{meter}{square \text{ } second}\right)} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} {\color{rgb(125,164,120)} \dfrac{50.93}{5940.0}}} \times {\color{rgb(125,164,120)} \left(\dfrac{meter}{square \text{ } second}\right)}\)
\(\text{Or}\)
\(1.0 \cdot {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \left(\dfrac{m}{s^{2}}\right)} = {\color{rgb(20,165,174)} x} \cdot {\color{rgb(125,164,120)} \dfrac{50.93}{5940.0}} \cdot {\color{rgb(125,164,120)} \left(\dfrac{m}{s^{2}}\right)}\)
\(\text{Cancel SI units}\)
\(1.0 \times {\color{rgb(89,182,91)} \dfrac{1609.344}{3.6 \times 10^{3}}} \cdot {\color{rgb(89,182,91)} \cancel{\left(\dfrac{m}{s^{2}}\right)}} = {\color{rgb(20,165,174)} x} \times {\color{rgb(125,164,120)} \dfrac{50.93}{5940.0}} \times {\color{rgb(125,164,120)} \cancel{\left(\dfrac{m}{s^{2}}\right)}}\)
\(\text{Conversion Equation}\)
\(\dfrac{1609.344}{3.6 \times 10^{3}} = {\color{rgb(20,165,174)} x} \times \dfrac{50.93}{5940.0}\)
Switch sides
\({\color{rgb(20,165,174)} x} \times \dfrac{50.93}{5940.0} = \dfrac{1609.344}{3.6 \times 10^{3}}\)
Isolate \({\color{rgb(20,165,174)} x}\)
Multiply both sides by \(\left(\dfrac{5940.0}{50.93}\right)\)
\({\color{rgb(20,165,174)} x} \times \dfrac{50.93}{5940.0} \times \dfrac{5940.0}{50.93} = \dfrac{1609.344}{3.6 \times 10^{3}} \times \dfrac{5940.0}{50.93}\)
\(\text{Cancel}\)
\({\color{rgb(20,165,174)} x} \times \dfrac{{\color{rgb(255,204,153)} \cancel{50.93}} \times {\color{rgb(99,194,222)} \cancel{5940.0}}}{{\color{rgb(99,194,222)} \cancel{5940.0}} \times {\color{rgb(255,204,153)} \cancel{50.93}}} = \dfrac{1609.344 \times 5940.0}{3.6 \times 10^{3} \times 50.93}\)
\(\text{Simplify}\)
\({\color{rgb(20,165,174)} x} = \dfrac{1609.344 \times 5940.0}{3.6 \times 10^{3} \times 50.93}\)
Rewrite equation
\(\dfrac{1.0}{10^{3}}\text{ can be rewritten to }10^{-3}\)
\(\text{Rewrite}\)
\({\color{rgb(20,165,174)} x} = \dfrac{10^{-3} \times 1609.344 \times 5940.0}{3.6 \times 50.93}\)
Solve \({\color{rgb(20,165,174)} x}\)
\({\color{rgb(20,165,174)} x}\approx52.138574514\approx52.1386\)
\(\text{Conversion Equation}\)
\(1.0\left(\dfrac{mile}{hour \times second}\right)\approx{\color{rgb(20,165,174)} 52.1386}\left(\dfrac{knot}{minute}\right)\)
