Corinne and aretha are having a 26-mile race. corinne gave aretha a head start by letting her begin 3.5 miles in front of the start line. their distances past the start line as the race has progressed can be represented by linear functions and are shown in the table and graph below. how many minutes after the start of the race will corinne catch aretha?

From the table, the speed of Corinne is given by



From the graph, the speed of Aretha is given by



The distance from the starting point of Corinne at any time t is given by D = 0.125t while the distance from the starting point of Aretha at any time t is given by D = 3.5 + 0.1t

Let t be the number of minutes after the start of the race when Corinne catchs Aretha, then

0.125t = 3.5 + 0.1t
0.025t = 3.5
t = 3.5 / 0.025 = 140

Therefore, the number of minutes after the start of the race that Corinne will catch Aretha is 140 minutes.