Two brothers start at the same time from 2 places 20 km apart.If they walk in the same direction ,the elder brother overtakes the younger in 10 hours but if they walk in opposite directions they meet in 2 hours.Find the rates in which they walk
Answers
Let the rate of the elder brother = 
Let the rate of the younger brother = 
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The elder brother has to have the faster rate
in order to catch up with the younger brother
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Also, when they walk in opposite directions,
they must be walking towards each other, or
else they would never meet
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Let  = distance the elder brother has
to travel to catch younger brother
Walking in same direction:
Equation for younger brother:
(1) 
Equation for elder brother:
(2) 
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Walking towards each other:
Think of this as the elder brother moving
at the sum of their speeds and the
younger brother not moving
(3) 
------------------------
Substitute (2) into (1)
(1) 
(1) 
(1) 
and
(3) 
--------------------------
Add (1) and (3)


and, since
(3) 
(3) 
(3) 
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The eldest brother's rate is 6 km/hr
The younger brother's rate is 4 km/hr
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check:
(2) 
(2)  km
and
(1) 
(1) 
(1)  km
OK