Question

How do you write each rate as a unit rate: $14$ hours in $2$ weeks?

Answer 1

Hint: The word ‘unit’ means one. If we say a unit amount of something, we mean to say that the amount is in terms of one. We will find the time in unit week, that is one week. Similarly, the week will be changed to a day.

Complete step by step answer:
Let us consider the given rate, $14$ hours in $2$ weeks.
We know that the terms given here are even numbers. So, they are multiples of $2.$
Also, if we have $14$ hours in $2$ weeks, then we want to find the amount of time we have in a unit amount of week.
That is, we want to find the amount of time we have in one week which is unity.
Now, in one week, we will have $7$ hours.
Since $1\times 2=2,$ $1=\dfrac{2}{2}.$ Similarly we will get $7\times 2=14$ which implies $7=\dfrac{14}{2}.$
Using the above relations, we will get $14$ hours in $2$ weeks $=7$ hours in $1$ week.
Now we got the week in units.
We are asked to change each rate as a unit rate.
Let us think about one week. We know that one week has $7$ days.
So, if we substitute this, we will get $7$ hours in $7$ days.
Let us divide both the quantities with $7,$ we will get $1$ hour in one day.

Hence the unit rate is $1$ hour in $1$ day $=1hour/day.$

Note: We can write the given statement as $14$ hours$/2$ weeks. This can be changed to $7$ hours/week. That is $7$ hours/$7$ days. This will be changed to $1$ hour/day.