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A policeman, who is 80 m away from a thief, starts chasing him. The th

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Bunuel
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A policeman, who is 80 m away from a thief, starts chasing him. The th [#permalink] New post   29 Jan 2021, 09:30
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A policeman, who is 80 m away from a thief, starts chasing him. The thief is running at a speed of 10 m/s. After exactly 8 seconds, the distance between them is 40m. What is the policeman’s speed?

(a) 10.5 m/s
(c) 12 m/s
(c) 15 m/s
(b) 17 m/s
(c) 25 m/s
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C
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Re: A policeman, who is 80 m away from a thief, starts chasing him. The th [#permalink] New post   29 Jan 2021, 09:51
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There are 2 ways we can go about solving this

(1) By the concept of Relative Speed, when 2 objects are moving in the same direction, the net effect is the difference between the speeds.

Let the policeman's speed = x m/s.

Then Time = Distance / Relative Speed

8 = 40 / (x - 10)

8x - 80 = 40

8x = 120

x = 15 m/s


(2) In 8 seconds the thief has run 8 * 10 = 80 m. Therefore the total distance run by the thief = 80 + 80 = 160 m

Let the speed of the policeman = x m/s. The distance covered by the policeman = 8x

After 8 seconds the policeman is 40 m behind the thief, which means the distance covered by the policeman = 160 - 40 = 120m

8x = 120

x = 15 m/s


Option C

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Re: A policeman, who is 80 m away from a thief, starts chasing him. The th [#permalink] New post   29 Jan 2021, 10:32
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In 8 seconds the distance between the thief and the policeman reduced by 40 meters, or 5 meters per second. So the speed of police is 5 m/s higher than that of the thief - 15 m/s. C)
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Re: A policeman, who is 80 m away from a thief, starts chasing him. The th [#permalink] New post   24 Dec 2021, 02:21
I'm always on the side of those who would have forgotten the formulas and methods in this case the RELATIVE SPEED.

With visualization you can determine that the policeman traveled 40m more than the thief.

Since we have the speed and time for the thief then the distance covered by the thief is 10m/s times 8s = 80m.

since the policeman traveled 40m more the the policeman distance is 80 + 40 = 120m

And since we have the time 8 seconds then we can find the speed that is 120 / 8 = 15m/s
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Re: A policeman, who is 80 m away from a thief, starts chasing him. The th [#permalink]
24 Dec 2021, 02:21
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