on a straight road of length 90 km, a Thief escape on a motorcycle at 30 kilometre per hour. an hour later a policeman starts the

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1. Answer:

   First, the patrol will reach the thief after 1h 40min.

   Step-by-step explanation:

   Thief:

   [tex]v_t=30\frac{km}{h}\\\\t-time[/tex]

   Policeman:

   [tex]v_{p1}=70\frac{km}{h}\\\\t-1-time[/tex]

   Patrol:

   [tex]v_{p2}=60\frac{km}{h}\\\\t-1-time[/tex]

   [tex]v=\dfrac{d}{t}\to d=vt[/tex]

   [tex]d-distance[/tex]

   Thief & policeman

   [tex]v_tt=v_{p1}(t-1)[/tex]

   [tex]30t=70(t-1)\\\\30t=70t-70\\\\30t-70t=-70\\\\-40t=-70\\\\t=\dfrac{-70}{-40}\\\\t=\dfrac{7}{4}\\\\t=1\dfrac{3}{4}\\\\t=1.75(h)[/tex]

   Thief & patrol

   [tex]v_tt+v_{p2}(t-1)=90[/tex]

   [tex]30t+60(t-1)=90\\\\30t+60t-60=90\\\\90t=90+60\\\\90t=150\\\\t=\dfrac{150}{90}\\\\t=\dfrac{5}{3}\\\\t=1\dfrac{2}{3}(h)[/tex]

   [tex]1\dfrac{2}{3}<1\dfrac{3}{4}[/tex]

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