Question 42574
Let r and j be their respective speeds.
Well if they ride toward each other and met in 1 hour, they must have a combined speed of 30 mph, since they were 30 miles apart...thus
r + j = 30
Now, Roberto overtakes Juana in 6 hours, meaning he must be going 5 mph faster to make up the 30 miles in 6 hours...thus
r = j + 5
Substituting this r into the first equation, we get
j+5 + j = 30
2j + 5 = 30
2j = 25
j = 12.5
and then
r = 17.5