Question

How do you express as a unit rate: 2400 miles in 48 hours?

Answer 1

Hint: We first explain the process of expressing the unit rate using a unitary system. We divide 2400 by 48 to find the unit rate in the form of $\text{m/h}$. We simplify the fraction to find the solution in integer form.

Complete step-by-step answer:
We have to find the unit rate for the given expression of 2400 miles in 48 hours.
In this case the unit rate means the number of miles for 1 hour instead of 48 hours.
We use the concept of unitary system where the unitary method is a method in which we find the value of a unit and then the value of a required number of units. The unitary method is also used to find the value of a single unit from a given multiple.
We use the given expression where it’s provided that 2400 miles in 48 hours.
It means in 1 hour it will be the division of 2400 by 48.
Therefore, the faction form will be $\dfrac{2400}{48}$.
The rate in 1 hour will be $\dfrac{2400}{48}$ miles.
For the fraction $\dfrac{2400}{48}$, the G.C.D of the denominator and the numerator is 48.
\[\begin{align}
  & 2\left| \!{\underline {\,
  48,2400 \,}} \right. \\
 & 2\left| \!{\underline {\,
  24,1200 \,}} \right. \\
 & 2\left| \!{\underline {\,
  12,600 \,}} \right. \\
 & 2\left| \!{\underline {\,
  6,300 \,}} \right. \\
 & 3\left| \!{\underline {\,
  3,150 \,}} \right. \\
 & 1\left| \!{\underline {\,
  1,50 \,}} \right. \\
\end{align}\]
Now we divide both the denominator and the numerator with 48 and get $\dfrac{{}^{2400}/{}_{48}}{{}^{48}/{}_{48}}=\dfrac{50}{1}=50$.
The unit rate for 2400 miles in 48 hours is $50\text{ m/h}$.

Note: We can also break the fraction in the multiplication form of two integers. The 2400 can be broken in $2400=24\times 100$ and 48 as $48=24\times 2$.
The division becomes
$\dfrac{2400}{48}=\dfrac{24\times 100}{24\times 2}=\dfrac{100}{2}=50$.