Question : A thief steals an item and escapes, running at a speed of 15 km/h. A policeman arrives at the spot of the crime after 4 minutes and immediately starts chasing the thief. 16 minutes after the policeman started to chase the thief, there was still a gap of 200 m between the two. At what distance from the spot of the crime will the policeman catch up with the thief and what is the speed of the policeman?
Option 1: 5.5 km; 16.5 km/h
Option 2: 6 km; 18 km/h
Option 3: 6.5 km; 19.5 km/h
Option 4: 5 km; 15 km/h
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Correct Answer: 6 km; 18 km/h
Solution :
Distance travelled by thief before police started chasing him = 15 × $\frac{4}{60}$ = 1 km
Distance travelled by the thief in 16 minutes after police started chasing him
= 15 × $\frac{16}{60}$ = 4 km
In 16 minutes, the gap between the thief and the policeman will be reduced by
= 1000 - 200 = 800 m
So, the remaining gap of 200 m will be covered in = $\frac{200}{800}$ × 16 = 4 minutes
$\therefore$ Distance covered by thief in 4 minutes = $15\times\frac{4}{60}$ = 1 km
Hence, total distance covered by thief before getting caught = 1 + 4 + 1 = 6 km
Now, the speed of the policeman = $\frac{\text{Distance}}{\text{Time}} = \frac{6\ \mathrm{km} \times60}{(16+4)\ \mathrm{hr}}$ = 18 km/h
Hence, the correct answer is '6 km, 18 km/h'.
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