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

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

Calculation Breakdown

Set up the equation

1.0 (\frac{m i l e}{s q u a r e s e c o n d}) = x (\frac{i n c h}{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{m i l e}{s q u a r e s e c o n d}) = 1609.344 (\frac{m e t e r}{s q u a r e s e c o n d}) = 1609.344 (\frac{m}{s^{2}})

Right side: 1.0 (\frac{i n c h}{h o u r \times s e c o n d}) = \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} (\frac{m e t e r}{s q u a r e s e c o n d}) = \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} (\frac{m}{s^{2}})

Insert known values into the conversion equation to determine

x

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

Insert known values =>

1.0 \times 1609.344 \times (\frac{m e t e r}{s q u a r e s e c o n d}) = x \times \frac{2.54 \times 10^{- 2}}{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 1609.344 \cdot (\frac{m}{s^{2}}) = x \cdot \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} \cdot (\frac{m}{s^{2}})

Cancel SI units

1.0 \times 1609.344 \cdot (\frac{m}{s^{2}}) = x \times \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} \times (\frac{m}{s^{2}})

Conversion Equation

1609.344 = x \times \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}}

Switch sides

x \times \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} = 1609.344

Isolate

x

Multiply both sides by

(\frac{3.6 \times 10^{3}}{2.54 \times 10^{- 2}})

x \times \frac{2.54 \times 10^{- 2}}{3.6 \times 10^{3}} \times \frac{3.6 \times 10^{3}}{2.54 \times 10^{- 2}} = 1609.344 \times \frac{3.6 \times 10^{3}}{2.54 \times 10^{- 2}}

Cancel

x \times \frac{2.54 \times 10^{- 2} \times 3.6 \times 10^{3}}{3.6 \times 10^{3} \times 2.54 \times 10^{- 2}} = 1609.344 \times \frac{3.6 \times 10^{3}}{2.54 \times 10^{- 2}}

Simplify

x = \frac{1609.344 \times 3.6 \times 10^{3}}{2.54 \times 10^{- 2}}

Rewrite equation

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

Rewrite

x = \frac{10^{2} \times 1609.344 \times 3.6 \times 10^{3}}{2.54}

Simplify

x = \frac{10^{5} \times 1609.344 \times 3.6}{2.54}

Solve

x

x = 228096000 \approx 2.281 \times 10^{8}

Conversion Equation

1.0 (\frac{m i l e}{s q u a r e s e c o n d}) \approx 2.281 \times 10^{8} (\frac{i n c h}{h o u r \times s e c o n d})

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