Question

A policeman follows a thief, who is 150 metres ahead of him., and they run at the speed of 6 km/h and 5 km/h, respectively.What distance does the policeman cover to catch up with the thief?

• A. 880 metres
• B. 870 metres
• C. 890 metres
• D. 900 metres

Answer 1

Answer:

D. 900 metres

Let’s do it cleanly using fractions

Convert speeds into m/s

• Policeman:
  $6 \text{ km/h} = \frac{6 \times 1000}{3600} = \frac{5}{3} \text{ m/s}$
  

• Thief:
  $5 \text{ km/h} = \frac{5 \times 1000}{3600} = \frac{25}{18} \text{ m/s}$
  

  Relative speed

$\frac{5}{3} - \frac{25}{18} = \frac{30 - 25}{18} = \frac{5}{18} \text{ m/s}$

Time to catch

$\text{Time} = \frac{150}{5/18} = 150 \times \frac{18}{5} = 540 \text{ seconds}$

Distance covered by policeman

$\frac{5}{3} \times 540 = 900 \text{ m}$

Final Answer: 900 m