We have no information about his whereabouts in the first 30 minutes, but between 30 minutes and 75+30=105 minutes he is 200-150=50 miles nearer home. So time t=0 represents the time from his position 200 miles away from home. His speed is 50/75=⅔ miles/minute (40mph). If distance is d: d=200-⅔t where t is measured in minutes.
For example, when t=60 minutes (1hr), that is 90 minutes away from home, d=200-40=160 miles from home, in which case d=180+⅔T for 0≤T≤30, d=220-⅔T for T≥30.
We can use time away from home, T=t+30, so t=T-30, in place of t: d=200-⅔(T-30)=200-⅔T+20=220-⅔T. This equation would describe where he was at some time T measured from the start of his journey, assuming his speed was constant at 40mph and he was travelling in the same direction. When T=0 minutes (t=-30 minutes), d=220 miles from home, according to the equation. If he was travelling in the opposite direction, his starting position could have been 200-20=180 miles from home.
