At the beginning of a bicycle ride for charity Roberto and J

At the beginning of a bicycle ride for charity Roberto and Juana are 30 mi apart. If they leave at the same time and ride in the same direction, Roberto overtakes Juanna in 6 hrs. If they ride toward each other, they meet in 1 hr. What are their speed?

Solution

Let the speed of Juana =x
Let the speed of Roberto =y
The distance between them is 30miles.
If they leave at the same time and ride in the same direction, Roberto overtakes Juanna in 6 hrs
6y-6x = 30
6(y-x)= 30
y-x = 30/6
y-x = 5 ...(1)
If they ride toward each other, they meet in 1 hr.
1*x+1*y = 30
x+y = 30 ...(2)
(1)+(2)=> 2y = 35
y = 35/2
y = 17.5 miles/hr
Substituting in (1), we get
17.5-x = 5
17.5-5 = x
12.5 = x
x = 12.5 miles/hr