Question

A thief is spotted by a policeman from a distance of \(200 \)meters. The policeman starts chasing at a speed of \( 10 \frac{km}{h}\) while the thief is running at a speed of \( 8\frac{km}{h}\). After how much time (in minutes) will the thief be caught?

• A. \(3\)
• B. \(5\)
• C. \(6\)
• D. \(8\)

Answer 1

The Correct Option is C

The thief and the policeman are moving in the same direction in a straight line. The speed of the policeman is \(10 \frac{km}{h}\), and the speed of the thief is \(8 \frac{km}{h}\). Initially, the distance between them is \(200 \) meters. We want to determine when the policeman will catch up to the thief.

The relative speed of the policeman with respect to the thief is \(10 - 8 = 2 \frac{km}{h}\).

To solve this, we first convert the relative speed into meters per second:

\[2 \frac{km}{h} = \frac{2 \times 1000}{60 \times 60} \frac{m}{s} = \frac{2000}{3600} \frac{m}{s} = \frac{5}{9} \frac{m}{s}\]

Using the formula \( \text{Time} = \frac{\text{Distance}}{\text{Speed}} \), the time taken to cover the \(200\) meters is:

\[\text{Time} = \frac{200}{\frac{5}{9}} = 200 \times \frac{9}{5}\]

\[\text{Time} = 360 \text{ seconds}\]

Since the question asks for the time in minutes, convert seconds to minutes:

\[\text{Time} = \frac{360}{60} = 6 \text{ minutes}\]

Therefore, the thief will be caught in \(6\) minutes.