The total distance traveled was

(350 mi/hr)(8 hr + 7 hr) = (325 mi/hr)(7 hr) + (x mi/hr)(8 hr)

350*15 = 325*7 + 8x (divide out units of miles)

(350*15 - 325*7)/8 = x (subtract 325*7 from both sides, then divide both sides by 8)

(5250 - 2275)/8 = x (evaluate)

2975/8 = x

(350 mi/hr)(8 hr + 7 hr) = (325 mi/hr)(7 hr) + (x mi/hr)(8 hr)

350*15 = 325*7 + 8x (divide out units of miles)

(350*15 - 325*7)/8 = x (subtract 325*7 from both sides, then divide both sides by 8)

(5250 - 2275)/8 = x (evaluate)

2975/8 = x