Products of rations to convert meters per second to miles per hour

[new^2^physics]

Homework Statement

Which of the following products of ratios gives the conversion factors to convert meters per second (m/s) to miles per hour (mi/hr)

Homework Equations

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]

The Attempt at a Solution

I will try to solve all these EXCLUDING THE NUMBERS, so I can focus on units and how they cancel each other out.

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
= in/mi x cm/in = cm/mi x cm/in = cm2/ mi.in... WRONG
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
= in/mi x in/cm = in2/mi.cm = WRONG
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
= in/mi x cm/in = cm/mi x cm/m = cm2/ mi.m - WRONG
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x cm/m = mi/m x s/h... hmmm WRONG??
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x m/cm = mi.m/cm2 WRONG

Basically I am beyond confused and would deeply appreciate any direction or help

THANK YOU!

 

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Homework Statement

Which of the following products of ratios gives the conversion factors to convert meters per second (m/s) to miles per hour (mi/hr)

Homework Equations

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]

The Attempt at a Solution

I will try to solve all these EXCLUDING THE NUMBERS, so I can focus on units and how they cancel each other out.

a. [5280f/mi] x [12 in/f] x [2.54 cm/1 in] x [100 cm/1m] x [3600 s/1h]
= in/mi x cm/in = cm/mi x cm/in = cm2/ mi.in... WRONG
b. [5280f/mi] x [12 in/f] x [1 in/ 2.54 cm] x [1 m/100cm] x [1 h/3600s]
= in/mi x in/cm = in2/mi.cm = WRONG
c. [5280f/mi] x [12 in/f] x [2.54 cm/1in] x [100 cm/1m] x [1 h/3600s]
= in/mi x cm/in = cm/mi x cm/m = cm2/ mi.m - WRONG
d. [1 mi/5280f] x [1 f/12 in] x [1 in/2.54 cm] x [100cm/1m] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x cm/m = mi/m x s/h... hmmm WRONG??
e. [1 mi/5280f] x [1 f/12in] x [1 in/2.54cm] x [1m/100 cm] x [3600s/1h]
= mi/f x f/in = mi/in x in/cm = mi/cm x m/cm = mi.m/cm2 WRONG

Basically I am beyond confused and would deeply appreciate any direction or help

THANK YOU!

d is correct. I couldn't quite follow your work, but you reduced it properly to mi/m x s/h. You then only needed to multiply by m/s to get mi/h.