Timothy leaves home for skedunk 400 miles away. after 2 hours, he has to reduce his speed by 20 mph due to rain. if he takes 1 hour for lunch and gas, and reaches skedunk 9 hours after he left home, what was his initial speed?

The entire trip took him 9 hours.
It took him 1 hour for lunch and gas, so he drove for 8 hours.
He drove a total of 400 miles.
He drove the first x miles at a higher speed, s, for 2 hours.
Then he drove the rest of the distance, 400 - x miles, at a lower speed, s - 20, for 6 hours.

speed = distance/time

distance = speed * time

First part of the trip:

x = s * 2

x = 2s

Second part of the trip:

400 - x = (s - 20) * 6

400 - x = 6s - 120

Substitute x = 2s in the equation just above:

400 - 2s = 6s - 120

-8s = -520

s = 65

The initial speed is 65 mph.