Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm .

F ind the time when the distance between the two persons is least?

Question

Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm .

F ind the time when the distance between the two persons is least?

Saurabh Singh · Answer

at time t hours after 1:30

first person will be (7.5+5t) from O

second person will be (5t) from O

distance between two will be

(7.5+5t)^2 +(5t)^2

we need to minimize this

the plot would look like -->

179-428_MSP120920a0b008g4dh730c000035i9h49db4ih64aa.gif

so they are closest at 0.75 hours before 1:30

i.e 45 minutes before 1:30

i.e 12:45

Thanks & Regards

Saurabh Singh,

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B.Tech.

IIT Kanpur

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Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm . F ind the time when the distance between the two persons is least?

Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm .

F ind the time when the distance between the two persons is least?

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