Question

How do you convert $ 42$ miles per hour to miles per minute?

Answer 1

Hint: First, convert from miles per hour to miles per minute then turn the result upside-down to get the reciprocal.
Using ratio in fractional format
$ = \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}}}}$
But there are $ 60$ minutes in an hour so we have:
$ \Rightarrow \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}}}} = \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}} \times {\text{60}}}}$
$ = \dfrac{{{\text{distance in miles}}}}{{{\text{time in minutes}}}}$
We apply this formula.
\[1\]minute $ = 60$ seconds
$ 1$ hour $ = 60$ minutes

Complete step-by-step solution:
The given information is $ 42$ miles per hour.
To convert miles per hour to miles per minute.
$ 42$ miles per hour$ = \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}}}}$ hence, we get
$ = \dfrac{{42}}{1}$
But there are $ 60$ minutes in an hour so we have:
$ \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}}}} \to \dfrac{{{\text{distance in miles}}}}{{{\text{time in hours}} \times {\text{60}}}}$
In minutes this is:
$ = \dfrac{{42}}{{{\text{1 hour}}}}$
$ 1$ hour $ = 60$ minutes
So we apply in the fraction, hence we get
$ = \dfrac{{42}}{{1 \times 60}}$
Now multiply $ 60$ by$ 1$ , hence we get
$ = \dfrac{{42}}{{60}}$ Minutes
But we need a $ 1$ minute so we have to change the $ 60$ minutes to $ 1$ minute.
For multiplying and dividing, what we do to the bottom we also do to the top to maintain the correct ratio.
Hence we get,
$ \Rightarrow \dfrac{{42}}{{60}} = \dfrac{{42 \div 60}}{{60 \div 60}}$
Change divide into the multiplication in RHS (Right Hand Side), hence we get
$ \Rightarrow \dfrac{{42}}{{60}} = \dfrac{{42}}{{60}} \times \dfrac{{60}}{{60}}$
We cancel the same number in numerator and denominator, hence we get
$ = \dfrac{{42}}{{60}}$
Divide $ 42$ by$ 62$ , hence we get
$ \dfrac{{42}}{{60}} = \dfrac{{0.7}}{1} \to \dfrac{{{\text{miles}}}}{{{\text{minute}}}}$
In $ 1$ minute the distance traveled is $ 0.7$ miles $ (\dfrac{7}{{10}}{\text{mile}})$

Note: To convert the desired units and remove the unwanted units, construct a fraction that will put minutes in the denominator, while eliminating the unwanted unit hours from the denominator.
In general, multiply the value and units by fractions that have the units you want in the right places, with the units you don’t want in the opposite places.
Converting hour to minute:
$ 1hr \times 60$
Converting minute to second:
$ 1\min \times 60$