Question 118242: At the beginning of the Alay Lakad, Rizza and Angel are 30 km apart. If they leave at the same time and walk in the same direction, Rizza overtakes Angels in 60 hours. If they walk towards each other, they meet in 5 hours. What are their speeds?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Rizza and Angel are 30 km apart. If they leave at the same time and walk in the same direction, Rizza overtakes Angels in 60 hours. If they walk towards each other, they meet in 5 hours. What are their speeds?
:
Let x = R's walking speed
Let y = A's walking speed
:
Walking the same direction equation; write a distance equation
Dist = time * speed
:
R's dist - 30 km = A's distance
60x - 30 = 60y
60x - 60y = 30
Simplify divide equation by 30
2x - 2y = 1
:
Walking towards each other equation (they are 30 km apart):
Write another distance equation: Dist = time * speed
R's dist + A's dist = 30 km
5x + 5y = 30
Simplify, divide equation by 5
x + y = 6
:
Use elimination, mult above equation by 2 add to equation: 2x - 2y = 1:
2x + 2y = 12
2x - 2y = 1
------------ adding eliminates y
4x = 13
x = 13/4
x = 3.25 km/hr is R's speed
:
Find y using equation x + y = 6
3.25 + y = 6
y = 6 - 3.25
y = 2.75 km/hr is A's speed
:
:
Check using the 1st equation:
60x - 30 = 60y
60(3.25) - 30 = 60(2.75)
195 - 30 = 165
and using the 5x + 5y = 30 equation
5(3.25) + 5(2.75) =
16.25 + 13.75 = 30; confirms our solutions
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