# Time and Distance Questions

FACTS  AND  FORMULAE  FOR  TIME  AND  DISTANCE

1.

2. x km/hr =

3. x m/sec =

4. If the ratio of the speeds of A and B is a:b , then the ratio of the times taken by them to cover the same distance is or b : a

5. Suppose a man covers a certain distance at x km/ hr and an equal distance at y km/hr . Then, the average speed during the whole journey is $\frac{2xy}{x+y}$km/hr.

Q:

The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 35 kms. what was the total distance travelled in 12 hours?

 A) 456 kms B) 482 kms C) 552 kms D) 556 kms

Explanation:

Total distance travelled in 12 hours    =(35+37+39+.....upto 12 terms)
This is an A.P with first term, a=35, number of terms,
n= 12,d=2.
Required distance    = 12/2[2 x 35+{12-1) x 2]
=6(70+23)
= 552 kms.

67 17639
Q:

A thief is noticed by a policeman from a distance of 200 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?

 A) 100 m B) 150 m C) 190 m D) 200 m

Explanation:

Relative speed of the thief and policeman  =  (11 – 10) km/hr = 1 km/hr

Distance covered in 6 minutes  = (1/60) x 6 km   = 1/10 km = 100 m

Therefore, Distance between the thief and policeman = (200 – 100) m = 100 m.

37 11418
Q:

How long will a boy take to run round a square field of side 35 meters, If he runs at the rate of 9 km/hr?

 A) 50 sec B) 52 sec C) 54 sec D) 56 sec

Explanation:

Speed = 9 km/hr = 9 x (5/18) m/sec = 5/2 m/sec

Distance = (35 x 4) m = 140 m.

Time taken = 140 x (2/5) sec= 56 sec

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Q:

Two horses start trotting towards each other, one from A to B and another from B to A. They cross each other after one hour and the first horse reaches B, 5/6 hour before the second horse reaches A. If the distance between A and B is 50 km. what is the speed of the slower horse?

 A) 30 km/h B) 15 km/h C) 25 km/h D) 20 km/h

Explanation:

If the speed of the faster horse be ${f}_{s}$ and that of slower horse be ${s}_{s}$ then

${f}_{s}+{s}_{s}=\frac{50}{1}=50$

and       $\frac{50}{{s}_{s}}-\frac{50}{{f}_{s}}=\frac{5}{6}$

Now, you can go through options.

The speed of slower  horse is 20km/h

Since,   20+30=50

and  $\frac{50}{20}-\frac{50}{30}=\frac{5}{6}$

35 7479
Q:

A man walking at the rate of 5 km/hr crosses a bridge in 15 minutes. The length of the bridge (in metres) is

 A) 600 B) 750 C) 1000 D) 1250

Explanation:

speed    = (5x5/18)m/sec
= 25/18 m/sec.

Distance covered in 15 minutes    = (25/18 x 15 x 60)m
= 1250 m.

42 7465
Q:

Two trains A and B start simultaneously in the opposite direction from two points P and Q and arrive at their destinations 16 and 9 hours respectively after their meeting each other. At what speed does the second train B travel if the first train travels at 120 km/h

 A) 90 km/h B) 160 km/h C) 67.5 km/h D) None of these

Explanation:

$\frac{{s}_{1}}{{s}_{2}}=\sqrt{\frac{{t}_{2}}{{t}_{1}}}$

$⇒\frac{120}{{s}_{2}}=\sqrt{\frac{9}{16}}=\frac{3}{4}$

$⇒$${s}_{2}=160km/h$

26 7358
Q:

The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is

 A) 720 B) 180 C) 75 D) 65

Explanation:

The hour hand moves from pointing to 12 to pointing to half way between 2 and 3. The angle covered between each hour marking on the clock is 360/12 = 30. Since the hand has covered 2.5 of these divisions the angle moved through is 75.

13 6705
Q:

A man takes 6 hours 15 minutes in walking a distance and riding back to the starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride both ways, is

 A) 4 hours B) 4 hours 30 minutes C) 4 hours 45 minutes D) 5 hours

Explanation:

Time taken in walking both ways = 7 hours 45 minutes                     --------(i)

Time taken in walking one way and riding back= 6 hours 15 minutes-------(ii)

By equation (ii)*2 -(i), we have

Time taken to man ride both ways, = 12 hours 30 minutes - 7 hours 45 minutes

= 4 hours 45 minutes