Two straight tracks AOB and COD meet each other at right angles at point O. A person walking at a speed of 5 km/h along AOB is at the crossing O at 12 o'clock noon. Another person walking at the same speed along COD reaches the crossing O at 1:30 PM. If the time at which the distance between them is least is 12:T PM, then find T.
Text Solution
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45
Sol. The positions of the persons at 12:00 PM will be as shown in figure. such that OC = 5 × 
km = 
km
Velocity of man at C with respect to man at O will be along CE such that tan θ = 
= 1
∴ θ = 45°
∴ least distance = OE = OC sin 45° = 
km
time taken = 
= 
= 
hr.
So, the person will be closest at 12:45 PM
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