Samantha drove 168 miles in 3 1/2 hours. she than drove the next 2 1/4 hours at a rate of 5 miles an hour faster than the first rate. how many miles did samanha drive durigthe 5 3/4 hours?

3.5 hours = 168 mi 

We need to figure out the miles per hour pace first, before we move on any further. 

To do this, divide 3.5 on both sides so we get per ONE hour: 
3.5 hours/3.5 = 168 mi/3.5

1 hour = 48 mi

That means for the first 3.5 hours, Samantha drove at a pace of 48 miles per hour. If she were to drive 5 miles an hour faster the next 2.25 hours, that means she would be driving at 53 miles per hour.

Now we need to find the total number of miles Samantha drove.
For the first 3.5 hours, she drove 168 miles.

For the next 2.25 hours, she drove at a pace of 53 miles per hour.

If 53 mi = 1 hour, we need to multiply 2.25 on both sides to find out how many miles is 2.25 hours.

53 mi x 2.25 = 1 hour x 2.25

53(2.25) mi = 2.25 hours

Simplify

119.25 mi = 2.25 hours

That means Samantha drove 119.25 miles for those 2.25 hours.

To find the total number of miles, we need to add them up:

168 + 119.25 = 287.25

So Samantha drove a total of 287.25 miles during the 5.75 hours :)