I given my resulting answers but they don't seem to be right. I used recatngle area methods to try and solve them.
Roger runs a marathon. His friend Jeff rides behind him on a bicycle and clocks his speed every 15 minutes. Roger starts out strong, but after an hour and a half he is so exhausted that he has to stop. Jeff's data follows.
Time since start (min) 0 15 30 45 60 75 90
Speed (mph) 12 11 10 10 8 7 0
Assuming that Roger's speed is never increasing, give upper and lower estimates for the distance Roger ran during the first half hour.
upper = 15*(12+11)=345, lower= 15*(10+11)=315