SOLUTION: At the beginning of a walk, Roberto and Juanita are 5.5 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they w

Question 323663: At the beginning of a walk, Roberto and Juanita are 5.5 miles apart. If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours. If they walk toward each other, 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 the beginning of a walk, Roberto and Juanita are 5.5 miles apart.
If they leave at the same time and walk in the same direction, Roberto overtakes Juanita in 11 hours.
If they walk toward each other, they meet in 1 hour. What are their speeds?
:
Let r = Roberto's speed
Let j = Juanita's speed
:
Write a time equation for each scenario, simplify; (Time = dist/speed)
:
= 1; walking toward each other
multiply by (r+j)
5.5 = r + j
and
= 11; walking the same direction
multiply by r - j
5.5 = 11(r - j)
divide both sides by 11
.5 = r - j
:
Arrange the two simplified equation for elimination
r + j = 5.5
r - j = .5
-------------addition eliminates j, find r
2r = 6
r = 3 mph is Robert's speed
Find j
r + j = 5.5
3 + j = 5.5
j = 5.5 - 3
j = 2.5 mph is Juanita's speed
:
:
Check solution by finding the times using these values
5.5/(3-2.5) = 11
5.5/(3+2.5) = 1; confirms our solution

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