Question

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 chase at 70 km per hour. at the same time a patrol party starts from the other end at 60 kilometre per hour who will reach the thief first and after how much time​

Answer 1

Answer:

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

Step-by-step explanation:

Thief:

$v_t=30\frac{km}{h}\\\\t-time$

Policeman:

$v_{p1}=70\frac{km}{h}\\\\t-1-time$

Patrol:

$v_{p2}=60\frac{km}{h}\\\\t-1-time$

$v=\dfrac{d}{t}\to d=vt$

$d-distance$

Thief & policeman

$v_tt=v_{p1}(t-1)$

$30t=70(t-1)\\\\30t=70t-70\\\\30t-70t=-70\\\\-40t=-70\\\\t=\dfrac{-70}{-40}\\\\t=\dfrac{7}{4}\\\\t=1\dfrac{3}{4}\\\\t=1.75(h)$

Thief & patrol

$v_tt+v_{p2}(t-1)=90$

$30t+60(t-1)=90\\\\30t+60t-60=90\\\\90t=90+60\\\\90t=150\\\\t=\dfrac{150}{90}\\\\t=\dfrac{5}{3}\\\\t=1\dfrac{2}{3}(h)$

$1\dfrac{2}{3}<1\dfrac{3}{4}$