A thief steals a car at 1.30pm and drives it 45 km an hour. The theft is discovered at 2pm and the owner sets off in another car at 50km an hour. he will overtake the thief at what time?

Both thief and owner need to travel the same distance for the owner to catch thief. Also, the time taken by thief is 0.5 hours more than that taken by the owner to cover the same distance. 

 

Hence, let the owner take t hours to cover the distance. Thief will taken t + 0.5 hours to do the same. 

 

Now, 45(t+0.5) = 50t

45t + 22.5 = 50t 

22.5 = 5t 

t = 4.5 hours. 

 

hence, the owner will overtake thief after 4.5 hours i..e 2pm +4.5 hours = 6.30 pm