Question

A thief, after committing a theft, runs at a uniform speed of 50 m/ minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief?\

Answer 1

Speed of the theif is 50 m/min

In 2 mins, the theif covers 100 m.

After 2 mins, the policeman runs to catch him, so in the third minute the policeman covers 60 m.

In the third minute the thief would cover 150 m.

Now policeman increases his speed by 5 m/ min (Student be careful units for speed is 5 m/min NOT just metres)

So, in the fourth minute:

Distance covered by policeman = 60 + 65 = 125 m

Distance covered by thief = 200 m

In the fifth minute:

Distance covered by policeman = 125 + 70 = 195 m

Distance covered by thief = 250 m

In the sixth minute:

Distance covered by policeman = 195 + 75 = 270 m

Distance covered by thief = 300 m

In the 7th minute:

Distance covered by policeman = 270 + 80 = 350

Distance covered by thief = 350 m

Hence, after 7 minutes the policeman will catch the thief.

Answer 2

Answer:

According to the question,

Distance between thief and police after 2 minutes = 100 m

Police starts chasing thief with initial speed of 60 and increasing his speed by 5 m every minute.

Let the police chase the thief for t minutes.

Implies, thief covers total 100 + 50t m

Police runs with following pattern 60,65,70...

This is an Arithmetic Progression with a = 60, d = 5 & number of terms = t

t/2(2×60+(t−1)×5)=50t+100

t×(120+5t−5)=100t+200

5t

2

+15t−200=0

t

2

+3t−40=0

t={−3±

(9+160)}/2

=(−3±13)/2=+5

Implies, police will catch thief in 5 minutes