A car is traveling at 65 miles per hour
on the freeway.
The driver looks down at his cell phone for 12 seconds.
How far has the car traveled, in feet,
in the 12 seconds the driver wasn't watching the road?
Notice how the rate is given in miles per hour.
We want the distance in feet in 12 seconds,
which means for the first step,
we will convert the unit rate of 65 miles per hour
to the unit rate in feet per second.
We first write the rate of 65 miles per hour
in fraction form, which is 65 miles per, or over, one hour,
and now we multiply by unit fractions
to convert miles to feet and hours to seconds.
Let's first convert the miles to feet.
One mile is equal to 5,280 feet,
and since they want the units of miles to simplify out,
and right now we have miles in the numerator,
for the unit fraction, we must have miles in the denominator
and feet in the numerator.
And again, because one mile is equal to 5,280 feet,
the unit fraction is 5,280 feet over one mile.
Notice miles simplify out.
I now need to convert hours to seconds.
We will first convert hours to minutes.
Because we want hours to simplify out
and right now, we have hours in the denominator,
the next unit fraction, we must have hours in the numerator
and minutes in the denominator.
And since one hour's equal to 60 minutes,
the next unit fraction is one hour over 60 minutes.
Notice hours simplify out.
For the last unit fraction,
we need to convert minutes to seconds.
We want minutes to simplify out,
and therefore, for the next unit fraction,
we must have minutes in the numerator
and seconds in the denominator.
And since one minute is equal to 60 seconds,
the last unit fraction is one minute over 60 seconds.
And notice minutes simplify out.
And notice now we have the units of feet and seconds.
Multiplying the numerator, we have 65 times 5,280 feet.
In the denominator, we have 60 times 60 seconds.
And now, we'll go to the calculator.
In the numerator, we have 65 times 5,280.
Notice how we have the numerator in parentheses.
And then, divided by the denominator is parentheses,
which is 60 times 60.
Notice how the unit rate has a repeating decimal.
If we ran it to the hundredths place value,
or two decimal places, we'd have approximately
95.33 feet per second.
But we don't want to use a rounded unit rate
to find the distance traveled in 12 seconds,
so let's go back to the calculator
and find the exact simplified rate.
To do this, we press Math, Enter, Enter,
which gives us the exact fraction for the previous entry.
So the exact simplified rate would be
286 feet per three seconds.
So we shouldn't use the rounded unit rate
to find the distance traveled in 12 seconds,
because we'd have an error in the distance.
So we'll use the exact simplified rate
of 286 feet per three seconds
to determine the distance traveled in 12 seconds.
Remember, distance is equal to rate times time,
and therefore, the distance traveled in 12 seconds
is equal to the exact rate of 286 feet per three seconds
times the time of 12 seconds, which, as a fraction,
would have a denominator of one.
Notice the seconds simplify out,
leaving us with the distance in feet.
Also notice how three and 12 share a common factor of three,
so we can simplify.
There's one three in three and four threes in 12.
Now let's go to the calculator.
286 times four is equal to 1,144.
We could've also found this product without simplifying
by entering 286 divided by three in parentheses,
and then times 12.
And of course, we get the same result.
So now we know the distance traveled in 12 seconds
is 1,144 feet.
Let's write the answer as a complete sentence.
If a driver looks down at his cell phone for 12 seconds
traveling at 65 miles per hour,
the car will travel 1,144 feet during that time,
which is a little scary because that is longer
than three American football fields,
which would be 1,080 feet.
So the moral of the story here
is keep your eyes on the road,
and don't check your phone while driving.
It's not safe.