1this problem can be easily done through graphs .. by plotting the x t graphs of both ..
there will be a number of parallelograms for which to intersect at the same x finally we will get the same time i.e. 8/3 ...
Two tourists who are at a distance of 40 km from their camp must reach it together in the shortest possible time. They have one bicycle which they decide to use in turn. One of them started walking at a speed v_1=5\ \mathrm{km/h} and the other rode off on the bicycle at a speed v_2=15\ \mathrm{km/h}. The tourists agreed to leave the bicycle at intermediate points between which one walks and the other rides. How long will the bicycle remain unused?
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4 Answers
106let the initial time for which cycle is rode be t. then dist covered by A = 5t and by B = 15t .
Now B walks and till A reaches the cycle he has travelled a further distance 10t.in time 2t.
now in t more time A's displacement will be 30t from initial position and so will be B's
so min. time = 4t ..
so.. now.. 30t=40km ==> t = 4/3 hr
and the cycle remained unused for 2t i.e. 8/3 hr..
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