Final answer:
The slower cyclist is traveling at 12 mph and the faster cyclist is traveling at 16 mph, as they cover a total of 28 miles per hour together moving in opposite directions.
Step-by-step explanation:
To solve this problem, we need to find the speed of the two cyclists traveling in opposite directions where one is traveling at a rate 4 mph faster than the other. Since they are moving apart from the same point, their combined hourly distance would be the sum of their speeds. After 4 hours, they are 112 miles apart, which means together they cover 112 miles/4 hours = 28 miles per hour. If we designate x as the speed of the slower cyclist, then the faster cyclist travels at x + 4 mph. The sum of their speeds is x + (x + 4) = 2x + 4. Therefore:
2x + 4 = 28
Subtract 4 from both sides:
2x = 24
Divide by 2:
x = 12 mph
So, the slower cyclist's speed is 12 mph and the faster cyclist's speed is x + 4 = 16 mph.