Shortcut Trick
Time difference between the thief and the owner starting = 30 minutes = 0.5 hours.
Lead distance created by the thief = 80 × 0.5 = 40 km.
Relative speed (same direction) = 90 − 80 = 10 km/h.
Time to catch = Distance gap ÷ Relative speed = 40 ÷ 10 = 4 hours.
Catch time = 4:00 p.m. + 4 hours = 8:00 p.m.
∴ The correct answer is 8:00 p.m.
Alternate Method
40 km gapMeeting distanceAThief starts 3:30 pmOwner starts 4:00 pmBThief at 4:00 pmCCatch pointRelative Speed Chase Diagram
Given:
Speed of the thief = 80 km/h
Speed of the owner = 90 km/h
Time delay before discovery = 4:00 p.m. − 3:30 p.m. = 30 minutes = 0.5 hours
Formula Used:
Relative Speed (same direction) = Speed1 − Speed2
Time = Distance ÷ Relative Speed
Calculations:
⇒ Distance covered by the thief in 0.5 hours = 80 × 0.5 = 40 km
⇒ When the owner starts chasing at 4:00 p.m., the distance between them is 40 km.
⇒ Relative speed of the owner with respect to the thief = 90 − 80 = 10 km/h
⇒ Time required for the owner to cover this 40 km gap = 40 ÷ 10 = 4 hours
⇒ The owner starts chasing at 4:00 p.m.
⇒ The owner will catch the thief at 4:00 p.m. + 4 hours = 8:00 p.m.
∴ The correct answer is 8:00 p.m.
Additional Information
Relative Speed (Same Direction)
When two objects move in the same direction, their relative speed is the difference between their individual speeds: Srelative = S1 − S2.
Relative Speed (Opposite Direction)
When two objects move towards each other, their relative speed is the sum of their individual speeds: Srelative = S1 + S2.
Meeting Point Distance
The distance from the starting point to the meeting point can be found by multiplying the speed of the chasing object by the time taken to catch up: D = Schaser × Tcatch.