Question 42574: At the beginning of a bicycle race for charity, Roberto and Juana are 30 mi. apart. If they leave at the same time and ride in the same direction, Roberto overtakes Juana in 6 hr. If they ride toward each other, they meet in 1 hr. What are their speeds
Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website! 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
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