320+ Time and Distance Problems With Solutions And Explanation

Q:

In a race of 800m Kaushik gives Piyush a start of 200m and then loses the race by 20 seconds. What is the speed of Piyush and Kaushik respectively ? If the ratio of respective speeds be 3:2.

Answer

Let the speed of Kaushik be Sk and speed of Piyush be Sp and let the time taken by Piyush be t second then,

$\frac{Sk}{Sp} = \frac{\frac{800}{t + 20}}{\frac{600}{t}} = \frac{2}{3} (since given ratio)$

t = 20 s

Speed of Piyush = Sp = 600/20 = 30 m/s

and Speed of Kaushik = 800/40 = 20 m/s

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8 6276

Q:

Two trains 85 m and 75 m long are running in same direction with speeds of 62 km/hr and 44 km/hr respectively. In what time will the first train cross the second train ?

A) 22 sec	B) 32 sec
C) 42 sec	D) 52 sec

Answer & Explanation Answer: B) 32 sec

Explanation:

Given that,

1st train speed = 62 km/hr

2nd train speed = 44 km/hr

Hence the relative speed of two trains is : 62-44 = 18 km/hr = $18 \times \frac{5}{18}$ m/s = 5 m/s.

There fore, the first train crosses the second train i.e (85+75)mts of distance with a speed of 5m/s in,

time = $\frac{d i s \tan c e}{s p e e d} = \frac{85 + 75}{5}$ = 32 sec.

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8 6258

Q:

Kamal consistently runs 240 meters a day and on Saturday he runs for 400 meters. How many kilometers will he have to run in four weeks ?

A) 5.75 kms	B) 7.36 kms
C) 8.2 kms	D) 6.98 kms

Answer & Explanation Answer: B) 7.36 kms

Explanation:

Total running distance in four weeks = (24 x 240) + (4 x 400)

= 5760 + 1600

= 7360 meters

= 7360/1000

=> 7.36 kms

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7 6125

Q:

You drive to the store at 20 kmph and return by the same route at 30 kmph. Discounting the time spent at the store, what was your average speed ?

A) 25 kmph	B) 24 kmph
C) 26 kmph	D) 22 kmph

Answer & Explanation Answer: B) 24 kmph

Explanation:

Average speed=total distance/total time
Let distance to store be K
then, total time =(K/20)+(K/30)=K/12
and, total time =(2K)
so average speed= 2K / (K/12) = 24kmph.

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Q:

'K' cycled from A to B at 10 kmph and returned at the rate of 9 kmph. 'L' cycled both ways at 12 kmph. In the whole journey 'L' took 10 minutes less than 'K'. Find the distance between A and B ?

A) 32.1 km	B) 15.23 km
C) 3.75 km	D) 32.1 m

Answer & Explanation Answer: C) 3.75 km

Explanation:

Let 'd' be the distance between A and B
K -time = d/10 + d/9 = 19d/90 hours
L -time = 2d/12 = d/6 hours
We know that, 10 min = 1/6 hours
Thus, time difference between K and L is given as 10 minutes.
=> 19d/90 - d/6 = 1/6
=> (19d-15d)/90 = 1/6
=> 4d/90 = 1/6
Thus,
d= 15/4 km = 3.75 km.

hence the distance between A and B is 3.75 km.

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Q:

In a daily morning walk three persons step off together. their steps measure 75 cm, 80 cm and 85 cm respectively. What is the minimum distance each should walk so that thay can cover the distance in complete steps ?

A) 222 m 44 cm	B) 204 m
C) 201 m 21 cm	D) 208 m

Answer & Explanation Answer: B) 204 m

Explanation:

To find the minimum distance, we have to get the LCM of 75, 80, 85

Now, LCM of 75, 80, 85 = 5 x 15 x 16 x 17 = 20400

Hence, the minimum distance each should walk so that thay can cover the distance in complete steps = 20400 cms = 20400/100 = 204 mts.

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11 5769

Q:

Karthik walks at 5 km/hr and reaches his destination 8 min late. If he walks at 6 km/hr, he reaches his destination on time. What distance he will cover in given time ?

A) 10 kms	B) 8 kms
C) 6 kms	D) 4 kms

Answer & Explanation Answer: D) 4 kms

Explanation:

Let the actual distance be t kms

Now, According to the data,

$5 (t + \frac{8}{60}) = 6 t = > 5 (\frac{60 t + 8}{60}) = 6 t = > 60 t + 8 = 72 t = > 8 = 12 t = > t = 8 / 12 = 2 / 3 hrs$

Now, the total distance = 6t = 6 x 2/3 = 2 x 2 = 4 kms.

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Q:

If a girl cycles at 10 kmph, then she arrives at a certain place at 1 p.m. If she cycles at 15 kmph, she will arrive at the same place at 11 a.m. At what speed must she cycle to get there at noon?

A) 14 kmph	B) 13 kmph
C) 12 kmph	D) 11 kmph

Answer & Explanation Answer: C) 12 kmph

Explanation:

The distance is constant in this case.

Let the time taken for travel with a speed of 10 kmph be 't'.

Now the speed of 15 kmph is 3/2 times the speed of 10 kmph.

Therefore, time taken with the speed of 15 kmph will be 2t/3 (speed is inversely proportional to time)

Extra time taken = t - 2t/3 = t/3

=> 1pm - 11am = 2hrs

=> t/3 = 2h

=> t = 6 hrs.

Now, Distance = speed x time = 10 x 6 = 60 kms

Time he takes to reach at noon = 6 - 1 = 5 hrs

Now, Speed = 60/5 = 12 kmph.

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