Convert inch / (hour • minute) to mile / (hour • second)

Learn how to convert 1 inch / (hour • minute) to mile / (hour • second) step by step.

Calculation Breakdown

Set up the equation

1.0 (\frac{i n c h}{h o u r \times m i n u t e}) = x (\frac{m i l e}{h o u r \times s e c o n d})

Define the base values of the selected units in relation to the SI unit

(\frac{m e t e r}{s q u a r e s e c o n d})

Left side: 1.0 (\frac{i n c h}{h o u r \times m i n u t e}) = \frac{0.0254}{2.16 \times 10^{5}} (\frac{m e t e r}{s q u a r e s e c o n d}) = \frac{0.0254}{2.16 \times 10^{5}} (\frac{m}{s^{2}})

Right side: 1.0 (\frac{m i l e}{h o u r \times s e c o n d}) = \frac{1609.344}{3.6 \times 10^{3}} (\frac{m e t e r}{s q u a r e s e c o n d}) = \frac{1609.344}{3.6 \times 10^{3}} (\frac{m}{s^{2}})

Insert known values into the conversion equation to determine

x

1.0 (\frac{i n c h}{h o u r \times m i n u t e}) = x (\frac{m i l e}{h o u r \times s e c o n d})

Insert known values =>

1.0 \times \frac{0.0254}{2.16 \times 10^{5}} \times (\frac{m e t e r}{s q u a r e s e c o n d}) = x \times \frac{1609.344}{3.6 \times 10^{3}} \times (\frac{m e t e r}{s q u a r e s e c o n d})

Or

1.0 \cdot \frac{0.0254}{2.16 \times 10^{5}} \cdot (\frac{m}{s^{2}}) = x \cdot \frac{1609.344}{3.6 \times 10^{3}} \cdot (\frac{m}{s^{2}})

Cancel SI units

1.0 \times \frac{0.0254}{2.16 \times 10^{5}} \cdot (\frac{m}{s^{2}}) = x \times \frac{1609.344}{3.6 \times 10^{3}} \times (\frac{m}{s^{2}})

Conversion Equation

\frac{0.0254}{2.16 \times 10^{5}} = x \times \frac{1609.344}{3.6 \times 10^{3}}

Cancel factors on both sides

Cancel factors

\frac{0.0254}{2.16 \times {10^{5}}^{10^{2}}} = x \times \frac{1609.344}{3.6 \times 10^{3}}

Simplify

\frac{0.0254}{2.16 \times 10^{2}} = x \times \frac{1609.344}{3.6}

Switch sides

x \times \frac{1609.344}{3.6} = \frac{0.0254}{2.16 \times 10^{2}}

Isolate

x

Multiply both sides by

(\frac{3.6}{1609.344})

x \times \frac{1609.344}{3.6} \times \frac{3.6}{1609.344} = \frac{0.0254}{2.16 \times 10^{2}} \times \frac{3.6}{1609.344}

Cancel

x \times \frac{1609.344 \times 3.6}{3.6 \times 1609.344} = \frac{0.0254 \times 3.6}{2.16 \times 10^{2} \times 1609.344}

Simplify

x = \frac{0.0254 \times 3.6}{2.16 \times 10^{2} \times 1609.344}

Rewrite equation

\frac{1.0}{10^{2}} can be rewritten to 10^{- 2}

Rewrite

x = \frac{10^{- 2} \times 0.0254 \times 3.6}{2.16 \times 1609.344}

Solve

x

x \approx 0.000000263 \approx 2.6305 \times 10^{- 7}

Conversion Equation

1.0 (\frac{i n c h}{h o u r \times m i n u t e}) \approx 2.6305 \times 10^{- 7} (\frac{m i l e}{h o u r \times s e c o n d})

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