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Devanand’s house is 50 km West of Pradeep’s house. On Sunday morning, at 10 a.m., they leave their respective houses.
Under which of the following scenarios, the minimum distance between the two would be 40 km?
Scenario I: Devanand walks East at a constant speed of 3 km per hour and Pradeep walks South at a constant speed of 4 km per hour.
Scenario II: Devanand walks South at a constant speed of 3 km per hour and Pradeep walks East at a constant speed of 4 km per hour.
Scenario III: Devanand walks West at a constant speed of 4 km per hour and Pradeep walks East at a constant speed of 3 km per hour.
Scenario I : Devanand's position after $$t$$ hours is $$(50 - 3t)$$ km west of Pradeep's house, while Pradeep's position is $$4t$$ km south of his own house.
If $$d$$ is the distance between them, then
=> $$d^2 = (50 - 3t)^2 + (4t)^2$$
=> $$d^2 = 2500 - 300t + 25t^2$$
=> $$d^2 = 25 (t^2 - 12t + 36) + 1600$$
=> $$d^2 = 25 (t - 6)^2 + 1600$$
Thus, minimum distance is 40 km after 6 hours.
Thus, scenario I is possible
Scenario II & III are not possible as minimum distance in that case would be 50 km as after that distance will keep on increasing between the two.
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