Question

4. A thief saw a policeman from distance of 700 m and started
running. Thief could run 4.7 km in 41 minutes & policeman can
run the same distance in 34 minutes. Find the distance thief
had run before being caught.​

Answer 1

The distance thief  had run before being caught = 3400 m

Step-by-step explanation:

Given:

The initial distance between thief and policeman = 700 m

Thief can run 4.7 km in 41 minutes and policeman can run 4.7 km in 34 minutes

To find out:

The distance run by thief when he was caught

Solution:

The initial distance between thief and policeman = 700 m = 0.7 km

Speed = distance/time

Speed of thief = 4.7/41 km/min

Speed of policeman = 4.7/34 km/min

Let the thief ran a distance d before being caught

The time taken by both the policeman and thief will be same

Thus,

$\frac{d+0.7}{4.7/34}=\frac{d}{4.7/41}$

$\implies 34(d+0.7)=41d$

$\implies d(41-34)=34\times 0.7$

$\implies d=\frac{34\times 0.7}{7}$

$\implies d=3.4$ km

$\implies d=3400$ m

Hope this answer is helpful.

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Answer 2

Given :- A thief saw a policeman from distance of 700m and started running. Thief could run 4.7km in 41 minutes & policeman can run the same distance in 34 minutes. Find the distance thief had run before being caught.

Solution :-

→ Thief runs = 4.7 km = 4.7 * 1000 = 4700 m.

→ Time taken = 41 min. =

→ speed of thief = (Distance/time) = (4700/41) m / min.

similarly,

→ Policeman runs = 4.7 km = 4.7 * 1000 = 4700 m.

→ Time taken = 34 min.

→ speed of Policeman = (Distance/time) = (4700/34) m / min.

then,

→ usual speed in same direction = speed of Policeman - speed of thief = (4700/34) - (4700/41) ={4700(41 - 34)} /34*41 = (4700 * 7)/1394 = 23.6 m/min.

therefore,

→ Time taken by policeman to catch the thief = (Distance between them) / usual speed = (700/23.6) = 29.67 minutes.

hence,

→ Distance covered by thief before caught = speed * time = (4700/41) * 29.67 ≈ 3401 m = 3.4 km (Ans.)

∴ The distance thief had run before being caught is 3.4 km .

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