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

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The unit rate is 50 miles per hour

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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:

The target is

Linking this to the given values we have:

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'.

Divide top and bottom by 48

So the unit rate is 50 miles per hour

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This is just the same as:

Effectively this is the same process as in

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

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#### Answer:

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

This can then be viewed as the fraction

Since a fraction can be interpreted as division, we can divide

We previously established that this would be in miles per hour, so our final answer is

Describe your changes (optional) 200