A thief runs with a uniform speed of 100 m/min. After one minute, a policeman runs after the thief to catch him. He goes with a speed of 100 m min in the first minute and increases his speed by 10 m/min every succeeding minute. After how many minutes the policeman will catch the thief?
ARITHMETIC PROGRESSION
please solve it with steps
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after 5 minutes the police will catch the thief
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Hola there..
According to the question,
Speed of thief = 100 m/min
Speed of police man = 100 m/min in 1st minute and then increase it speed by 10 m/min
Let the time take to catch the thief be = 'x'
Distance travelled by thief = 100(x + 1)
Distance travelled by the police man = x/2(2×100 + (x - 1)10)
Both the distance will be equal so,
=> 100(x + 1) = x/2(200 + (x - 1)10)
=> 100x + 100 = x(100 + (x - 1)5)
=> 100x + 100 = 100x + 5x² - 5x
=> 5x² - 5x - 100 = 0
=> x² - x - 20 = 0
=> x² - 5x + 4x - 20 = 0
=> x(x - 5) + 4(x - 5) = 0
=> (x - 5)(x + 4) = 0
=> x = 5 or -4
As, the speed can't be negative so we will reject -4 as time.
Therefore, The policeman will catch the thief in 5 min.
Hope this helps....:)
According to the question,
Speed of thief = 100 m/min
Speed of police man = 100 m/min in 1st minute and then increase it speed by 10 m/min
Let the time take to catch the thief be = 'x'
Distance travelled by thief = 100(x + 1)
Distance travelled by the police man = x/2(2×100 + (x - 1)10)
Both the distance will be equal so,
=> 100(x + 1) = x/2(200 + (x - 1)10)
=> 100x + 100 = x(100 + (x - 1)5)
=> 100x + 100 = 100x + 5x² - 5x
=> 5x² - 5x - 100 = 0
=> x² - x - 20 = 0
=> x² - 5x + 4x - 20 = 0
=> x(x - 5) + 4(x - 5) = 0
=> (x - 5)(x + 4) = 0
=> x = 5 or -4
As, the speed can't be negative so we will reject -4 as time.
Therefore, The policeman will catch the thief in 5 min.
Hope this helps....:)
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