Question 356599: at a beginning of a bicycle ride for charity, Roberto and Juana are 30 miles apart. If they leave at the same time and ride in the same direction, Roberto evertakes Juana in 6 hours. If they ride toward eachother, they meet in 1 hour. What are their speeds?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! at a beginning of a bicycle ride for charity, Roberto and Juana are 30 miles apart.
If they leave at the same time and ride in the same direction, Roberto overtakes Juana in 6 hours.
If they ride toward each other, they meet in 1 hour. What are their speeds?
:
Let r = R's speed
Let j = J's speed
:
When they ride the same direction, their relative speed is (r-j)
When they ride towards each other, their relative speed is (r+j)
:
Write a distance equation for each scenario; (Dist = speed * time)
6(r-j) = 30
and
1(r+j) = 30
:
Simplify the 1st equation, divide both sides by 6 and,
you can use elimination with the 2nd equation
r - j = 5
r + j = 30
-------------adding eliminates j, find r
2r = 35
r = 
r = 17.5 mph is R's speed
then
17.5 + j = 30
j = 30 - 17.5
j = 12.5 mph is J's speed
:
:
Check solution using the 1st original equation
6(17.5 - 12.5) =
6(5) = 30; confirms our solution
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