(C) Initial distance between the policeman and the thief $= 400\, m$.Relative speed of the policeman with respect to the thief $= 9\, km/h - 5\, km/h

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(C) Initial distance between the policeman and the thief $= 400\, m$.Relative speed of the policeman with respect to the thief $= 9\, km/h - 5\, km/h = 4\, km/h$.Converting relative speed into $m/s$: $4 \times \frac{5}{18} = \frac{10}{9}\, m/s$.Time taken by the policeman to overtake the thief $= \frac{\text{Distance}}{\text{Relative Speed}} = \frac{400}{10/9} = 400 \times \frac{9}{10} = 360\, s$.Speed of the thief in $m/s = 5 \times \frac{5}{18} = \frac{25}{18}\, m/s$.Distance covered by the thief in $360\, s = \text{Speed} \times \text{Time} = \frac{25}{18} \times 360 = 25 \times 20 = 500\, m$.

Competitive Quantitative Aptitude Time and Distances Time and Distances

Medium

$A$ thief is spotted by a policeman from a distance of $400\, m$. When the policeman starts the chase,the thief also starts running. Assuming the speed of the thief is $5\, km/h$ and that of the policeman is $9\, km/h$,how far will the thief have run before he is overtaken by the policeman? (in $m$)

A
$400$
B
$600$
C
$500$
D
$300$

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Time and Distances

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Time and Distances

$A$ man travels $360 \, km$ in $4 \, hrs$,partly by air and partly by train. If he had travelled all the way by air,he would have saved $\frac{4}{5}$ of the time he was in train and would have arrived at his destination $2 \, hrs$ early. Find the distance he travelled by train (in $km$).

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In a flight of $600 \, km$,an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $200 \, km/hr$ and the time of flight increased by $30 \, minutes$. The duration of the flight is (in $hour$):

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$A$ person has to reach a certain place at a certain time. He finds that he will be $15 \text{ minutes}$ late if he walks at $4 \text{ km/h}$,and $10 \text{ minutes}$ earlier if he walks at $6 \text{ km/h}$. How far has he to walk? (in $\text{km}$)

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$A$ man crosses a stationary bus in $18\, s$. The same bus crosses a pole in $4\, s$. What is the ratio of the speed of the bus to the speed of the man?

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$A$ moving train crosses a man standing on a platform and a bridge of $300 \, \text{metres}$ long in $10 \, \text{seconds}$ and $25 \, \text{seconds}$ respectively. What will be the time taken by the train to cross a platform $200 \, \text{metres}$ long? (in $\text{seconds}$)

Medium

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$A$ man travels $360 \, km$ in $4 \, hrs$,partly by air and partly by train. If he had travelled all the way by air,he would have saved $\frac{4}{5}$ of the time he was in train and would have arrived at his destination $2 \, hrs$ early. Find the distance he travelled by train (in $km$).

In a flight of $600 \, km$,an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by $200 \, km/hr$ and the time of flight increased by $30 \, minutes$. The duration of the flight is (in $hour$):

$A$ person has to reach a certain place at a certain time. He finds that he will be $15 \text{ minutes}$ late if he walks at $4 \text{ km/h}$,and $10 \text{ minutes}$ earlier if he walks at $6 \text{ km/h}$. How far has he to walk? (in $\text{km}$)

$A$ man crosses a stationary bus in $18\, s$. The same bus crosses a pole in $4\, s$. What is the ratio of the speed of the bus to the speed of the man?

$A$ moving train crosses a man standing on a platform and a bridge of $300 \, \text{metres}$ long in $10 \, \text{seconds}$ and $25 \, \text{seconds}$ respectively. What will be the time taken by the train to cross a platform $200 \, \text{metres}$ long? (in $\text{seconds}$)

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