Step-by-step explanation:
she drove already 165 miles.
she will reach her destination, if she drives 4 more hours by going 65 miles/hour.
that would mean she would travel
65×4 = 260 miles
in these 4 hours.
so, the total trip is then 165 + 260 = 425 miles.
but what I find strange is that your teacher specified how long it took her to drive the first 165 miles.
as you can see above, it would make no difference for the calculation of the total trip length in miles.
this is either an attempt to confuse us, or the message is that Judy has to achieve an average of 65 miles/hour for the whole trip, and the problem definition was just imperfectly phrased.
if that is the case, then things look a bit different, as her average speed was only 165/3 = 55 miles/hour for the first 3 hours and 165 miles.
so,
(165 + x)/(3 + 4) hours = 65/hour
(165 + x)/7 hours = 65/hour
165 + x = 65 × 7 hours / hour = 65×7 = 455 miles
x = 455 - 165 = 290 miles
she would have to go
290 miles / 4 hours = 72.5 miles/hour
for these next 4 hours (and 290 miles) to reach an overall average speed of 65 miles/hour.
and the total trip would be then
165 + 290 = 455 miles
I am not sure, which your teacher wants here.
65 miles/hour average speed just for the next 4 hours, or to speed up that much for the next 4 hours that the overall trip average is then 65 miles/hour.
again, the phrasing of the problem definition suggests the first case, but the fact that the travel time for the first part of the trip is given could suggest the second case (as this information is not needed for the first case).
will have the form 
, where A and B are equivalent and factors that are multiplied in.
you will need to find a fraction which is a product of this: 