Discussion
The police noticed a thief from a distance of 300 m. Afraid of being caught by the police, the thief started running at 7 km/h. The police started chasing him at speed of 8 km/h and caught the thief. How much distance did the thief run before he was caught?
Answer: C
The thief ran 2100 m. The police close the gap at the difference of the speeds, 8 - 7 = 1 km/h.
\[ t = \frac{0.3}{1} = 0.3 \text{ h} \]\[ \text{distance} = 7 \times 0.3 = 2.1 \text{ km} \]\[ 2.1 \text{ km} = 2100 \text{ m} \]The police themselves ran 2400 m, which is the other option that sounds plausible; 1,800 m and 1,900 m do not fit the chase.
The police must make up 300 m at 1 km/h, so they run for 0.3 h and cover 8 × 0.3 = 2.4 km, which is 300 m more than the thief's 2.1 km. The question asks for the distance the thief ran, so 2400 m, the distance the police ran, is the wrong figure to pick.
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