Final answer:
To find the speed of each cyclist, the distance covered by both in 3 hours is equated to 96 miles. Solving the resulting equation indicates that the faster cyclist bikes at 17.5 mph and the slower at 14.5 mph.
Step-by-step explanation:
The question involves two cyclists racing towards each other from a distance of 98 miles apart. After traveling for 3 hours, they are 2 miles apart. To find out how fast each cyclist is biking, let's denote the speed of the faster cyclist as x mph. Consequently, the slower cyclist would be at x-3 mph. The total distance covered by both cyclists in 3 hours is 98-2=96 miles.
Setting up the equation, we have:
3x + 3(x-3) = 96
3x + 3x - 9 = 96
6x - 9 = 96
6x = 96 + 9
6x = 105
x = 17.5
Thus, the faster cyclist is biking at 17.5 mph and the slower cyclist at 17.5 - 3 = 14.5 mph.