Acar and cyclist start at 10 a. m. from the same point, headed in the same direction. the average speed of the car is 5 mph more than three times the average speed of the cyclist. in 1.5 hours, the car is 46.5 miles ahead of the cyclist. find the speed at which the cyclist is traveling. show all of your work.

Poor little person. 
Average speed of car = x 
Average speed of cyclist: y 
x = 3y+ 5 
After 1.5h, 
1.5x = 1.5y + 46.5 
To explain this, after 1.5 hours, the distant of the car is 46.5 away from the cyclist. (I know it's a bit confusing) 
Substitube 
1.5(3y + 5) = 1.5y + 46.5 
4.5y + 7.5 = 1.5y + 46.5 
3y = 39 
y = 13 
x = 3y+ 5 
x= 3(13) + 5 
x = 39 + 5 
x = 44 
Let's check. 
In 1.5 hours. the car has gone 
1.5(44) = 66 miles 
The cyclist has gone 
1.5(13) = 19.5 
66 - 19.5 = 46.5 
So it's right. 
I guess. 
Rate of cyclist is 13 mph.