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**Speed, Time & Distance**. This is also one of the important and easiest aptitude topics for banking, insurance and other competitive exams, where you will get a compulsory question. But the problem is, people tend to lose marks in Speed, Time and Distance topic due to negligence. I will explain how this happens. In the exam hall, we will be in a hurry mood to answer as many questions as possible. So we won't read the question properly. You need to check,

*in WHICH UNITS*they asked the answer. Some times they may ask the answer in Kmph, but you get your number in Mps. To confuse you, they will give both the numbers in options. So, instead of converting the units, we hurriedly mark the option of the families number, still assuming that our answer is correct. So you need to crosscheck the units before marking the answer. Okay, let's get into the details of today's lesson

**. Let's start with basic formulas. Write these down in your notebook. Hope you are already maintaining a separate notebook for these lessons.**

__Speed, Time and Distance__## Speed, Time and Distance Shortcuts

###
__Speed, Time & Distance Formulas__

__Speed, Time & Distance Formulas__

**1**. Speed = Distance / Time [S = D/T]

**2.**Distance = Speed x Time [D=S x T]

**3**. Time = Distance / Speed [T=D/S]

**4**. The units of speed = Kilometres per hour (Kmph) or Metres per second (Mps).

**5**. Kmph x (5/18) = Mps

**6**. Mps x (18/5) = Kmph

**7**. If two bodies are in movement and their speeds are 'X' units and 'Y' units, the resultant speed (which is called relative speed) is to be taken in the place of 'S in the first three formulas above.

Relative speed is

**X + Y**if they move in opposite direction**X-Y**if they move in same direction

**8**. If a train has to cross any another body, it has to cover a distance which is equal to the sum of its own length and that of the other body which it has to cross and this total is to be taken in the place of 'D' in the first three formulas. In case of the length of the other body is negligible, only the length of the train is to be taken.

**9**. Average speed = Total distance covered / Total time taken

**10**. In two cases of equal distances, the average speed = 2AB/(A+B) where A and B are the speeds.

**11**. In three cases of equal distances, the average speed = 3ABC (AB + BC + CA) where A, B and C are the speeds.

**12**. In four cases of equal distances, the average speed = 4ABCD / (ABC + BCD + CDA + DAB) where A, B, C and D are the speeds.

**13**. If a man covers a distance at two different speeds with late and / or early times,

The distance = (Difference in given late or early times in hours x Product of the speeds) / Difference of the speeds

= (∆t × π s)/∆s

and correct speed required = (∆t × π s)/(S2 × ∆t ±t1 ×∆s)

**Note**: Here you should use '

**+**' if

*t1*is early tie and '

**-**' if

*t1*is late time.

**14.**If the average speeds of a train including stoppages and excluding stoppages are given, the time in minutes for which the train stops for hour = (Difference in speeds x 60) / Higher speed

**15**. If a man walking at N/D of his usual speed in T minutes late or early, then the usual time taken by him = (N/(N~D)) ×T

**16**. If a train crosses two objects of '

*l*' and '

*L*' units in length in '

*t*' and '

*T*' times, then the speed =

*(l~L)/(t~T)*and the length of the train =

*(t(l~L)/(t~T)) - l*

**17**.

*is the speed at which an object moves*

__Down stream speed (DS)____along with__

*the flow of water.*

DS = X + Y, where X = Speed of the object in still (calm) water and Y = speed of the water

**18**.

__Upstream speed (US)__is the speed at which an object moves

__against__the flow of the water.

US = X-Y, where X = Speed of the object in still (calm) water and Y = speed of the water

**19**. Speed or Velocity of a man or a boat in still water = X = (DS + US) / 2

**20**. Speed or Velocity of Water or Flow or Stream or Current = Y = (DS - US) / 2

Now let's work with problems. As usual, I will explain one problem per model and share 3 problems of the same model for your practice.

###
__Speed, Time and Distance : Examples & Practice Problems__

__:__

**Model 1****The speed of a car is 40 kmph. What distance can it cover in 9 seconds ?**- 96 mts
- 100 mts
- 108 mts
- 120 mts
- None of these

**Solution :**

*****If you observe closely, in question they gave the speed in Kmph. But in answer options, they gave the speed in mts. So you should convert Kmph into Mph.

**Note : To convert Kmph into Mph, you need to multiply it with 5/18**

Here S = 40 kmph

t = 9 sec

d = s.t = 40 x (5/18) x 9 = 100 Mph

Let's work with another problem.

**2. The speed of a car is 60 kmph. What distance can it cover in 13.5 seconds ?**

- 96 mts
- 100 mts
- 108 mts
- 120 mts
- None of these

**Solution**:

= 60 x (5/18) x 13.5

**Note**: Decimal points always slow down your calculations. So to remove decimal point from 13.5, Multiply Numerator and Denominator with 10.

= 60 x (5/180) x 135

= 225

__Practice Problems on Model 1__**The speed of a car is 36 kmph. What distance can it cover in 9.6 seconds ?**- 96 mts
- 100 mts
- 108 mts
- 120 mts
- None of these
**The speed of a car is 80 kmph. What distance can it cover in 5.4 seconds ?**- 96 mts
- 100 mts
- 108 mts
- 120 mts
- None of these

__Model 2__:**A train can cover a distance of 243 km in 3 hours. What is its speed in meters / second ?**- 12.5
- 18
- 20
- 22.5
- None of these

**Solution :**

S = d/t

Here also the speed of the car given in Kmph but asked the answer in Mts. So,

= (243/3) x (5/18)

= 22.5 mps

__:__

**Practice Problems on Model 2****A train can cover a distance of 324 km in 4 hours. What is its speed in meters / second ?**- 12.5
- 18
- 20
- 22.5
- None of these
**A train can cover a distance of 360 km in 5 hours. What is its speed in meters / second ?**- 1.5
- 18
- 20
- 22.5
- None of these
**A train can cover a distance of 280.8 km in 4 hrs 20 min. What is its speed in meters / second ?**- 12.5
- 18
- 20
- 22.5
- None of these

**:**

__Model 3__**In what time can a car cover a distance of 360 km at 12 1/2 mps ?**- 5 hrs
- 8 hrs
- 10 hrs
- 20 hrs
- None of these

**Solution :**

t = d/s

(360 x 2 x 5) / (25 x 18) = 8 hrs

(360 x 2 x 5) / (25 x 18) = 8 hrs

__Practice Problems on Model 3__**In what time can a car cover a distance of 270 km at 15 mps ?**- 5 hrs
- 8 hrs
- 10 hrs
- 20 hrs
- None of these
**In what time can a car cover a distance of 1440 km at 20 mps ?**- 5 hrs
- 8 hrs
- 10 hrs
- 20 hrs
- None of these
**In what time can a car cover a distance of 960 km at 18 mps ?**- 5 hrs
- 8 hrs
- 10 hrs
- 20 hrs
- None of these

**:**

__Model 4__**A train 250 m long is running at 45 kmph. In what time can it pass a tree ?**- 15 sec
- 20 sec
- 30 sec
- 24 sec
- None of these

**Solution :**

t = d/s

= (250 x 18) / (45 x 5) = 20 sec

**:**

__Practice problems on Model 4__**A train 300 m long is running at 36 kmph. In what time can it pass a pole ?**- 15 sec
- 20 sec
- 30 sec
- 24 sec
- None of these
**A train 375 m long is running at 90 kmph. In what time can it pass a man ?**- 15 sec
- 20 sec
- 30 sec
- 24 sec
- None of these
**A train 336 m long is running at 42 kmph. In what time can it pass a railway signal ?**- 18 sec
- 20 sec
- 22.5 sec
- 24 sec
- None of these

**:**

__Model 5__**A train 600 m long moves at 36 kmph. In what time can it pass a bridge of 1200 m long ?**- 2 min
- 2.5 min
- 3 min
- 4 min
- None of these

**Solution :**

t = d/s

= ((600+1200) x 18) / (36x5)

= 180 sec

= 3 min

**Practice Problems on Model 5****A train 300 m long moves at 72 kmph. In what time can it pass a bridge of 420m long ?**- 36 sec
- 48 sec
- 1 min
- 1.2 min
- None of these
**A train 400 m long moves at 63 kmph. In what time can it pass a bridge of 440 m long ?**- 2 min
- 48 sec
- 1 min
- 1.2 min
- None of these
**A train 500 m long moves at 54 kmph. In what time can it pass a bridge of 2.2 km long ?**- 2 min
- 2.5 min
- 3 min
- 4 min
- None of these

**:**

__Model 6__**A train moving at a speed of 45 mps takes 12 sec to pass a man running at the rate of 5 mps in the same direction. The length of the train in meters is**- 350
- 392
- 420
- 450
- None of these

**Solution :**

d =s x t

= (45-5) x 12

= 480 m

*

**Speeds :**

**If the Second object is moving in**, you need to write__Same direction____Difference of speeds__**If the Second object is moving in**, you need to write the__Opposite direction____Sum of speeds__

__:__

**Practice Problems on Model 6****A train moving at a speed of 40 mps takes 10 sec to pass a man running at the rate of 5 mps in the same direction. The length of the train in meters is ?**- 350
- 392
- 420
- 450
- None of these
**A train moving at a speed of 48 mps takes 10 sec to pass a man running at the rate of 6 mps in the same direction. The length of the train in meters is ?**- 350
- 392
- 420
- 450
- None of these
**A train moving at a speed of 35 mps takes 15 sec to pass a man running at the rate of 5 mps in the same direction. The length of the train in meters is**- 350
- 392
- 420
- 450
- None of these

__:__

**Model 7****Two trains running on parallel lines are 450 m and 350 m long at 50 kmph and 40 kmph respectively. In what time can they pass each other if they are moving in the same direction ?**- 4 min
- 4 min 12 sec
- 4 min 20 sec
- 4 min 36 sec
- None of these

**Solution :**

t = d/s

= (800 x 18) / (10x5) = 288 sec

4mins 48 secs

= (800 x 18) / (10x5) = 288 sec

4mins 48 secs

**Practice Problems on Model 7****Two trains running on parallel lines are 450 m and 470 m long at 52 kmph respectively. In what time can they pass each other if they are moving in the same direction ?**- 4 min
- 4 min 12 sec
- 4 min 20 sec
- 4 min 36 sec
- None of these
**Two trains running on parallel lines are 300 m and 350 m long at 49 kmph and 40 kmph respectively. In what time can they pass each other if they are moving in the same direction ?**- 4 min
- 4 min 12 sec
- 4 min 20 sec
- 4 min 36 sec
- None of these
**Two trains running on parallel lines are 510 m and 330 m long at 50 kmph and 38 kmph respectively. In what time can they pass each other if they are moving in the same direction ?**- 4 min
- 4 min 12 sec
- 4 min 20 sec
- 4 min 36 sec
- None of these

__:__**Model 8****Two trains running on parallel lines are 600 m and 900 m long at 40 and 50 kmph respectively. In what time can they pass each other if they are moving in opposite direction ?**- 54 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these

**Solution**:

t = d/s

= (1500x18) / (190x5) = 60 sec = 1 min

= (1500x18) / (190x5) = 60 sec = 1 min

**Note**:- If the Distance is in
**Kms**then Speed also should be in**Kms**. - If the Distance is in
**Meters**then the Speed also should be in**Meters**.

**Practice Problems on Model 8 :****Two trains running on parallel lines are 600 m and 450 m long at 40 and 30 kmph respectively. In what time can they pass each other if they are moving in opposite direction ?**- 54 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these
**Tow trains running on parallel lines are 400 m and 500 m long at 22 and 23 kmph respectively. In what time can they pass each other if they are moving in opposite direction ?**- 54 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these
**Two trains running in parallel lines are 600 m and 750 m long at 20 and 20.5 kmph respectively. In what time can they pass each other if they are moving in opposite direction ?**- 54 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these

**:**

__Model 9__**A train of 600 m long moves at 54 kmph can cross another train of 750 m long moving in the same direction in 4 1/2 min .What is the speed of the second train ?**- 36 kmph
- 40 kmph
- 48 kmph
- 50 kmph
- None of these

**Solution :**

*** Here the first one crosses the second one (by moving in the same direction). So, the speed of first train is high**

S = d/t

S1-S2 = d/t

= (1350 m / 270 sec) x (18/5) = 18

54-? = 18 => 36

__Practice Problems on Model 9__:**A train of 600 m long moves at 55.2 kmph can cross another train of 450 m long moving in the same direction in 2 1/2 min. What is the speed of the second train ?**- 36 kmph
- 40 kmph
- 48 kmph
- 30 kmph
- None of these
**A train of 600 m long moves at 76 kmph can cross another train of 480 m long moving in the same driection in 2 2/5 min. What is the speed of the second train ?**- 36 kmph
- 40 kmph
- 48 kmph
- 50 kmph
- None of these
**A train of 900 m long moves at 90 kmph can cross another train of 1200 m long moving in the same direction. What is the speed of the second train ?**- 36 kmph
- 40 kmph
- 48 kmph
- 50 kmph
- None of these

__:__

**Model 10****A train 300 m long passes a pole in 25 sec. How long will it take to pass a bridge of 360 m long ?**- 42 sec
- 1 min
- 1 min 12 sec
- 42 sec
- None of these

**Solutions :**

s = d/t = 300/25 = 12

s = 660/12 = 55 sec

**2nd Method :**

300m ------> 25 sec

300+360 = 660m ----> ?

=> (660 / 300) x 25 = 55 Sec

**Practice Problems on Model 10**:**A train 250 m long passes a pole in 20 sec. How long will it take to pass a bridge of 275 m long ?**- 54 sec
- 1 min
- 1 min 12 sec
- 42 sec
- None of these
**A train 320 m long passes a pole in 24 sec. How long will it take to pass a bridge of 480 m long ?**- 42 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these
**A train 270 m long passes a pole in 18 sec. How long will it take to pass a bridge of 360 m long ?**- 42 sec
- 1 min
- 1 min 12 sec
- 2 min
- None of these

__Model 11__:**A train covers a distance in 24 min if it runs at 48 kmph. What should it speed be if it has to cover the same distance in 16 mins ?**- 45 kmph
- 60 kmph
- 72 kmph
- 90 kmph
- None of these

**Solution :**

24 min --------> 48 kmph

16 min ---------> ?

=> more / less = (24/16) x 48 = 72 kmph

**Practice Problems on Model 11****A train covers a distance in 20 min if it runs at 50 kmph. What should it speed be if it has to cover the same distance in 12 min 30 sec ?**- 45 kmph
- 60 kmph
- 72 kmph
- 80 kmph
- None of these
**A train covers a distance in 25 min if it runs at 48 kmph. What should its speed be if it has to cover the same distance in 20 min ?**- 45 kmph
- 60 kmph
- 72 kmph
- 90 kmph
- None of these
**A train covers a distance in 30 min if it runs at 60 kmph. What should its speed be if it has to cover the same distance in 20 min ?**- 45 kmph
- 60 kmph
- 72 kmph
- 90 kmph
- None of these

__:__

**Model 12****A car has to cover 450 kms in 10 hrs. It covered 2/5 of the distance in 3/5 of the time. At which speed should it move to cover the rest of the distance in the rest of the time ?**- 90 kmph
- 60 kmph
- 72 kmph
- 90 kmph
- None of these

**Solution :**

Remaining distance = d = (1 - 2/5) x 450 = (3/5) x 450 = 270

t = (1 - 3/5) x 10 = (2/5) x 10 = 4 hrs

=> required speed = remaining distance / remaining time = 270 / 4 = 67.5 = 67 1/2 kmph

**Practice problems on Model 12**:**A car has to cover 550 kms in 10 hrs. It covered 3/5 of the distance in 3/4 of the time. At which speed should it move to cover the rest of the distance in the rest of the time ?**- 99 kmph
- 60 kmph
- 72 kmph
- 88 kmph
- None of these
**A car has to cover 480 kms in 9 hrs. It covered 2/5 of the distance in 2/3 of the time. At which speed should it move to cover the rest of the distance in the rest of the time ?**- 99 kmph
- 60 kmph
- 72 kmph
- 88 kmph
- None of these
**A car has to cover 900 kmps in 12 hrs. It covered 9/10 of the distance in 7/12 of the time. At which speed should it move to cover the rest of the distance in the rest of the time ?**- 99 kmph
- 60 kmph
- 72 kmph
- 90 kmph
- None of these

**:**

__Model 13__**A student walks from his house at 2.5 kmphs and reaches his school by 5 min late and if he walks at 3 kmph, he will reach his school by 10 min early. What is the distance between the school and his house ?**- 2.25 kms
- 2.75 kms
- 3.25 kms
- 3.75 kms
- None of these

**Solution :**

= (∆t × π s)/∆s

Distance = (Difference in given late or early times in hours x Product of the speeds) / Difference of the speeds

= (1/4) x ((1/2)x3)/(1/2)) = 15/4 [15 mins ---> 1/4 hr]

= 3 3/4 km

**Practice Problems on Model 13**:**A student walks from his house at 3 kmph and reaches his school by 5 min late and if he walks at 3.25 kmph, he will reach his school by 1 min early. What is the distance between the school and his house ?**- 2.25 kms
- 2.75 kms
- 3.25 kms
- 3.75 kms
- None of these
**A student walks from his house at 3 kmph and reaches his school by 30 min late and if he walks at 2 1/2 kmph, he will reach his school by 10 min 30 sec late. What is the distance between the school and his house ?**- 2.25 kms
- 2.75 kms
- 3.25 kms
- 3.75 kms
- None of these
**A student walks from his house at 2 kmph and reaches his school by 30 sec late and if he walks at 3 kmph, he will reach his school by 1 min early. At which speed should he go to reach the school in time ?**- 2.25 kmph
- 2.75 kmph
- 2.5 kmph
- 2.4 kmph
- None of these

__:__

**Model 14****A man goes to a place at 24 kmph and returns at 40 kmph. What is the average speed ?**- 32 kmph
- 30 kmph
- 32.5 kmph
- 35 kmph
- None of these

**Solution :**

If the distances are equal, Avg speed = 2AB / (A+B)

= (2 x 960) / 64 = 30 kmph

**Practice Problems on Model 14****A man goes to a place at 60 kmph and returns at 42 kmph. What is the average speed ?**- 51kmph
- 47 2/17 kmph
- 48 6/17 kmph
- 49 7/17 kmph
- None of these
**A man goes to a place at 80 kmph and returns at 56 kmph. What is the average speed ?**- 62 kmph
- 61 2/17 kmph
- 65 15/17 kmph
- 66 13/17 kmph
- None of these
**A man goes to a place at 100 kmph and returns at 125 kmph. What is the average speed ?**- 109 2/9 kmph
- 111 1/9 kmph
- 113 4/9 kmph
- 114 5/9 kmph
- None of these

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