Question

A quarter horse often excels at running races of \[\dfrac{1}{4}\] mile or less. How many feet is that?

Answer 1

Hint: To solve this problem firstly we should know the conversion methods as we cannot relate miles and feet directly, so we initially convert miles to yards and then we can convert yards to feet. During the solve this particular problem it is necessary to know the standard values of conversion.

Complete step-by-step solution:
In the given problem,
We don’t have any equation in the table that relates miles and feet directly. However, you can convert miles to yards first. Then you can convert yards to feet.
Now we can multiply the given measurement by the conversion factor.
The given value \[\dfrac{1}{4}\] miles can be written as follows,
\[\dfrac{1}{4}\] Miles = 0.25 miles
We know from the standards of conversion from miles to yards that,
1 mile = 1, 760 yards
So, 0.25 miles can be written as follows,
\[\begin{align}
  & 0.25miles\times \dfrac{1760yards}{1miles} \\
 & \\
 & \Rightarrow 0.25\times 1760yards \\
\end{align}\]
\[\Rightarrow 440yards\]
We also know from the standards of conversion from yards to feet that,
1yards = 3 feet,
So we can write the obtained 440 yards as below,
\[\begin{align}
  & 440yards\times \dfrac{3feet}{1yards} \\
 & \\
 & \Rightarrow 440\times 3feet \\
\end{align}\]
\[\Rightarrow 1320feet\]
From the above calculations we can write that a length of \[\dfrac{1}{4}\] miles is equal to 1,320 feet.

Note: For these calculations one should be well versed with the conversion from one unit to another like miles to yards and yards to feet, if a student gets the conversion factors wrong then the whole answer will become wrong.