Question

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

Answer 1

50 mph

Explanation:

Usually when given a speed and asked to find the unit rate, your end result should distance per time. In this case it would be miles per hour because these are the units you are given, but in other situations it could be feet per minute or meters per second.

To begin, we can set up the given information as a ratio of `2400:48`.
This can then be viewed as the fraction `2400/48`.
Since a fraction can be interpreted as division, we can divide `2400` by `48` and the end result is `50/1`, which is equivalent to `50`.
We previously established that this would be in miles per hour, so our final answer is `50` mph.

Answer 2

The unit rate is 50 miles per hour

Explanation:

`color(blue)("Using first principles")`

`color(green)("The explanation bit")`

The clue is in the units used: miles per hour

where 'per' means for each, so 'per mile' is the 'unit' we are looking for:

Mathematically this is written as: `("miles")/("hour")`

The target is `("miles")/("1 hour")`

Linking this to the given values we have:

`("miles")/("hours") -> 2400/48`

To change the bottom number of 48 into 1 we divide by 48 but what we do to the bottom we also do to the top to maintain the correct proportions. That is, for multiply and divide. Addition or subtraction 'messes this up'.

`color(green)("The calculation bit")`

Divide top and bottom by 48

`("miles")/("hours") -> 2400/48-=(color(red)(2400-:48))/(48-:48) = 50/1" ........."Equation(1)`

So the unit rate is 50 miles per hour
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using the shortcut method")`

`("miles")/("hours") -> 2400/("48 hours") = ("miles")/("1 hour")`

This is just the same as:`" miles" =color(red)(2400/48) =50`

Effectively this is the same process as in `Equation(1)`

The only difference is that this is understood to be miles per hour.

So instead of just writing 50 you write 50 miles per hour