320+ Time and Distance Problems With Solutions And Explanation

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

Answer & Explanation Answer: A) 100 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:

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

Answer & Explanation Answer: B) 7.2

Explanation:

Speed = $(\frac{600}{5 \times 60}) m / s e c$ = 2 m/sec = 2 x (18/5) km/hr = 7.2 km/hr

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311 67564

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

Answer & Explanation Answer: C) 552 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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340 60787

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

Answer & Explanation Answer: C) 71.11 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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148 55073

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

Answer & Explanation Answer: B) 160 km/h

Explanation:

$\frac{s_{1}}{s_{2}} = \sqrt{\frac{t_{2}}{t_{1}}}$

$\Rightarrow \frac{120}{s_{2}} = \sqrt{\frac{9}{16}} = \frac{3}{4}$

$\Rightarrow$ $s_{2} = 160 k m / h$

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159 44993

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

Answer & Explanation Answer: 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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54 38373

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

Answer & Explanation Answer: 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 $\frac{50}{20} - \frac{50}{30} = \frac{5}{6}$

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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

Answer & Explanation Answer: 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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