An ant moved for several seconds and covered 3 mm in the first second and 4 mm more in each successive second than in its predecessor.If the any had covered 1 mm in first second and 8 m more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than 6 mm but less than 30 mm. Find the time for which the ant moved (in seconds)

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Let ant move for t secondCase I: St​ when ant move 3 m min first second and 4 m min in each second.Sn​=2t​[2(3)+(t−1)4]Case II: St​ when ant move 1 mm in first second and 8 mm in each secondSt​=2t​[2(v)+(t−1)8]ATQ6<2t​[2+(t−1)8]−2t​[6+(t−1)4]<306<2t​[−8+4t]<306<[−4t+2t2]<30From option putting t=4 Only condition is satisfied6<−16+32<306<16<30

Question Text	An ant moved for several seconds and covered $3$ mm in the first second and $4$ mm more in each successive second than in its predecessor.If the any had covered $1$ mm in first second and $8$ m more in each successive second, then the difference between the path it would cover during the same time and the actual path would be more than $6$ mm but less than $30$ mm. Find the time for which the ant moved (in seconds)
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