SOLUTION: Two brothers start at same time from two places 20 kms apart. If they walk in same
direction, elder brother overtakes the younger in 10 hrs, but if they walk in opposite
directio
Question 879989: Two brothers start at same time from two places 20 kms apart. If they walk in same
direction, elder brother overtakes the younger in 10 hrs, but if they walk in opposite
directions, they meet in 2 hrs. Find the rates at which they walk. Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website! 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)
==============
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
