Question

A thief escaped from police custody. Since he was sprinter he could clock $40km/hr$. The police realized it after $3$ hr and started chasing him in the same direction at $50km/hr$. The police had a dog which could run at $60km/hr$. The dog could run to the thief and then return to the police and then would turn back towards the thief. If kept on doing so till the police caught the thief. Find the total distance travelled by the dog in the direction of the thief.

• A. $720km$
• B. $600km$
• C. $660km$
• D. $360km$

Answer 1

The correct option is C $660km$

Speed of thief $=40kmperhr=v_t$

Speed of police $=50kmperhr=v_p$

Police started after 3hrs of start of thief

$50t=40t+40\left(3\right)$

$\therefore t=12hr$

Time taken by police to catch thief $=12hr$

Distance travelled by dog $=12\times 60$

$=720km$

$\Rightarrow$ Distance travelled by police + To and from distance by Dog $=720$

Distance travelled by police $=50\times 12$

$=600km$

$\Rightarrow$ $600+2\left(\text{from distance by dog}\right)=720$

"Fro" distance (distance from thief to police)="to"distance(distance from police to thief after once it returns)

$600+2\left(\text{'fro' distance by dog}\right)=720$

$\therefore$ 'fro' distance $=60$

$\therefore$ Total distance towards thief $=600{+}^{\prime }to"distance$

$=720-$ 'fro' distance

$=660km$