# 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:

A person crosses a 600 m long street in 5 minutes, What is his speed in km per hour?

 A) 3.6 B) 7.2 C) 8.4 D) 10

Explanation:

Speed =   = 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr

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Q:

A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. The average speed for the first 320 km of the tour is

 A) 35.55 km/hr B) 36 km/hr C) 71.11 km/hr D) 71 km/hr

Explanation:

Total time taken    = (160/64 + 160/8)hrs
= 9/2 hrs.

Average speed    = (320 x 2/9) km.hr
= 71.11 km/hr.

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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.

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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.

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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:

$s1s2=t2t1$

$⇒120s2=916=34$

$⇒$$s2=160km/h$

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Q:

A man reaches his office 20 min late, if he walks from his home at 3 km per hour and reaches 30 min early if he walks 4 km per hour. How far is his office from his house ?

 A) 20 km B) 16 km C) 14 km D) 10 km

Explanation:

Let distance = x km.
Time taken at 3 kmph : dist/speed = x/3 = 20 min late.
time taken at 4 kmph : x/4 = 30 min earlier
difference between time taken : 30-(-20) = 50 mins = 50/60 hours.
x/3- x/4 = 50/60
x/12 = 5/6
x = 10 km.

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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:

The ratio between the speeds of two trains is 7: 8. If the second train runs 400 kms in 4 hours, then the speed of the first train is ?

 A) 83.5 km/hr B) 84.5 km/hr C) 86.5 km/hr D) 87.5 km/hr

Explanation:

Let the speeds of two trains be 7X and 8X km/hr.

8x = 400/4

=> x= 12.5 km/hrX=4004=>X=12.5Km/hr

So speed of first train is 12.5*7 = 87.5 km/hr