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Chaser starts some time after the leader: catch time, distance or speed

This type of question, asked 5 times: 14 Jul 2023 S2, 19 Jul 2023 S2, 24 Jul 2023 S1, 25 Jul 2023 S4, 26 Jul 2023 S1. All 5 questions below, oldest first.

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  1. Question 1

    14 Jul 2023 S2

    74
    A thief steals a van at 3:00 a.m. and drives it at a speed of 57 km/h. The thief is discovered at 4:00 a.m. and the owner starts the chase with another van at a speed of 76 km/h. At what time will he catch the thief?

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  2. Question 2

    19 Jul 2023 S2

    69
    A thief committed a crime and escaped from the spot at a speed of 12 m/h. A Security guard started chasing him 20 minutes after the thief started running and caught him in the next 20 minutes. What is the speed (in m/h) of the Security guard?

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  3. Question 3

    24 Jul 2023 S1

    69
    A policeman chases a thief. The speeds of the policeman and the thief are 8 km/h and 6 km/h, respectively. If the policeman started 10 minutes late, at what distance he will catch the thief?

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  4. Question 4

    25 Jul 2023 S4

    64
    A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief; there is still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up the thief and what is the speed (in km/h) of the policeman?

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  5. Question 5

    26 Jul 2023 S1

    68
    A thief steals an item and escapes, running at 20 km/h. A policeman arrives at the spot of the crime after 6 minutes and immediately starts chasing the thief. 24 minutes after the policeman started to chase the thief, there is still a gap of 400 m between the two. At what distance from the spot of crime would the policeman catch up with the thief, and what is the speed at which the policeman ran?

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