A theif...

Question

A thief flees to San Francisco and heads towards Los Angeles driving at a rate of 80 km/h. Five minutes after the thief lease, a deputy sheriff begins chasing the thief and drives that 100 km/h. How long will it be before the deputy sheriff catches up with the thief?

Answer 1

speed of thief=80 km/hr = 80 

distance covered by thief =x

time taken by thief = t min

speed of thief in km/min=80/60  km/m ≈ 1.33 km/min

 distance/time= speed

 

x/ t =1.33

x =1.33 t            ________ eq 1

 

speed of deputy sheriff = 100 km/hr

distance = x

time = (t-5) minute

speed of deputy sheriff in km/min =100/60 ≈1.67 km /min

 

x/t-5 =1.67

x = 1.67(t-5)     ______ eq 2

 

 

equate both x

 

1.33 t =1.67(t-5)

 

1.33t =1.67t - 8.35

 

0.34t=8.35

 

t≈ 24.6 min

 

time taken by deputy sheriff ≈24.6-5≈19.5 minutes

 

So it takes approximatly 19.5 minutes to deputy sherrif catches up thief