A man runs after a thief 10 mins after the thief has started running. They run at the rates of 8 km/hr and 5 km/hr respectively. When and where will the thief be overtaken?

20 min, 3.5 km

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18 min, 5 km

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16.66 min, 2.22 km

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18 min, 5/3 km

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Solution

The correct option is C
16.66 min, 2.22 km

The thief starts running 10 minutes before at a speed of 5 km/hr.

Distance covered in 10 min = $5 \times \frac{10}{60}$ = 0.833 km. The thief is already 0.833 km ahead.

Now the man and thief both are running in the same direction and the difference between their speeds is 3 km/hr.

We know that, time = $\frac{D i s t a n c e}{S p e e d}$
So, time required = $\frac{0.833}{3}$ = 0.2777 hour = 16.66 min

The distance would be = $8 \times 0.2777$ = 2.22 km.

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