Question 255101
first we must know the formula for distance in terms of speed and time
rt=d
we will consider this little trip as two different trips taken one after another with a total time of 5 hours and a total distance of 250 miles.
rt+rt=d
We know the total time was 5 hours and the parts add up to 5
So let t = the second part and 5-t the first part
[We could also have said s for first part and t for second part
t+s=5
then we would have to solve for s in terms of t
s=5-t does that look familiar?
and substitute. But the first method is a shortcut.]

30*(5-t)+55*(t)=250
So just multiply it out and solve for t
t will be the time at 55 mph
[If we wanted to solve for just the 30 mph part we would have set t for it and 5-t for the 55 ]


30*(5-t)+55*(t)=250
150-30t+55t=250
subtract 150 from both sides
add 55t-30t
then you will have to divide that to get t alone on one side