Time, Speed & Distance II

Study Notes  on Time and Speed For SBI PO

(1).Relation between distance ,time and speed:
Distance = speed x Time

(2).To convert speed of any object from KMPH to MPS multiply the speed by = 1000 / 3600 = 5 / 18

(3).To convert speed of any object from MPS to KMPH multiply the speed by = 3600 / 1000 = 18/ 5

(4).If the speed ratio of A and B is a:b then ratio of time to cover certain distance is = 1/a : 1/b = b : a

(5).If a person covers certain distance with speed x KMPH and return back with speed y  KMPH then his average speed throughout the journey is
Average speed = 2xy/(x+y)KMPH

(6).
If a certain distance is covered with 3 diffrent speed x KMPH, y KMPH and z KMPH then average speed throughout the journey is
Average speed = 3xyz/(xy+yz+zx)KMPH

(7).
If 2 different distances covered with speed x KMPH and y KMPH respectively but required same time the then average speed throughout the journey is
Average speed = (x+y)/2 KMPH

(8).If 2 trains start at the same time from different points suppose A and B respectively toward each other and after crossing if they take a and b seconds time resp to reach at B and A point then
(A’s speed) : (B’s speed) = Öb : Öa

Formulae based on Train Problems
Relative Speed (Train Problems):

(9)If two trains are moving in the same direction with speed x KMPH and y KMPH where x>y in that case their relative speed is given as :(x-y) KMPH

(10)
If two trains are moving in the opposite direction with speed x KMPH and y KMPH in that case their relative speed is given as: (x+y) KMPH

Quant Quiz on Time and Distance

1.Walking at 7/8th  of his usual speed, a man reached his destination 16 minutes later than the time he usually takes to reach his destination. Find the usual time taken by him  to reach his destination.

(a) 1 hour, 44 minutes
(b) 1 hour, 52 minutes
(c) 1 hour, 36 minutes
(d) 1 hour, 40 minutes

2.A person goes to office by train. He walks to the railwy station closest to his home to catch the train. One day, he walked at 4 km/hr and missed the train by 5 minutes. The next day, he walked at 6 km/hr and reached the station 7 minutes before the arrival of the train. find the distance between his home and the station. 
(a) 2.4 km
(b) 1.8 km
(c) 3.6 km
(d) 3 km

3. Ashok covered a distance of 225 km as follows. He covered the first 15 km at 45 km/hr, the next 120 km at 60 km/hr and the remaining journey at 90 km/hr. Find his average speed for the journey of 225 km. 
(a) 65 km/hr
(b) 67.5 km/hr
(c) 70 km/hr
(d) 73.5 km/hr

4. A person went from P to Q, at an average speed of a km/hr, from Q to R at an average speed of b km/hr, and from R to S at an average speed of the c km/hr. If PQ = QR = RS, then the average speed of the person for traveling from P to S was
(a) (a + b + c)/ 3
(b) 3abc/(ab + bc + ca)
(c) 3abc/(a + b + c)
(d) 3(ab + bc + ca)/(a + b + c)

5. Car P starts from town X toward town y. Car Q stars from Y towards X. Both the cars start simultaneously and travel their meet after journeys at uniform speeds. XY = 200 km. Both cars meet after 2 hours. If P and Q had travelled in the same direction both the cars would have met in 4 hours. Find the speed of P. 
(a) 60 kmph
(b) 85 kmph
(c) 75 kmph
(d) 80 kmph

6. Train P overtakes train Q double its length and travelling at half of speed of train P in 36 seconds. Train P crosses train R going in the opposite direction at double its speed in 8 seconds. If the speed of train P is 72 kmph then the length of train R is ………..
(a) 330 m
(b) 360 m
(c) 390 m
(d) 420 m

7. A 480 m long train was travelling at 72 km/hr. It took 32 seconds to cross a cyclist travelling in the same direction as the train. Find the speed of the cyclist. 
(a) 12 km/ph
(b) 15 km/ph
(c) 18 km/ph
(d) 9 km/ph

8. A train, 180m long, crossed a 120 m long platform in 20 seconds, and another train travelling at the same speed crossed an electric pole in 10 seconds. In how much time will they cross each other when they are travelling in the opposite direction.?
(a) 11 sec
(b). 13 sec
(c) 12 sec
(d) 14 sec

9. On a circular track, time taken by A and B to meet when travelling in the opposite directions is 1/4 of time taken when they travel in the same direction. Find the ratio of their speeds? 
(a) 5: 3
(b) 6 : 5
(c) 4 : 3
(d) 3 : 2

10. How long will three persons starting at the same point and travelling at 4 km/hr, 6 km/hr and 8 km/hr around a circular track 2 km long take to meet at the starting point? 
(a) 1/2hr
(b) 1hr
(c) 1.5 hrs
(d) 2 hrs

Answers with Explanation
1. (b)         Ratio
Speed  8 : 7
Time  7 : 8
1 = 16
7 = 7 X 16 = 112 min
= 1 hr 52 min

2. (a) Let S1 = 4 kmph, S2 = 6 kmph
Distance =  (S1 ×  S2)/ (S1-S2) X total time in hr
Distance =  (4 ×6)/ (6- 4)  x (7+5)/60
= (4 ×6)/2  ×  1/5 = 2.4 km

3. (b) Average speed  = Total distance / Total time
=  225/(15/45 + 120/60 + 90/90)  = 67.5 km/h

4. (b) by above concept No. 6

5. (c) Let speed of car P = S1
& speed of car Q = S2
From Ist case:
2S1 + 2S2 = 200   – (i)
From 2nd case, When cars travelled in Same direction
200/ (S1 – S2) = 4
4 S1 – 4 S2 = 200   (ii)
From Equation  (i) & (ii)
S1 = 75 kmph

6. (b) For Train P
length = L, Speed = 72 kmph
For train Q
length = 2L, Speed = 36 kmph
(L + 2L)/(72 – 36)X5/18
L= 120 meter
For train R
Speed = 2 X 72 = 144 kmph
& length = x meter
(120 + x) / (144 + 72)X5/18    = 8
x  = 360 meter

7. (c)  Let speed of cyclist  = x kmph
480/(72 – x) X 5/18 = 32
x = 18 kmph

8. (a) Let speed of 1st train = x kmph
(180 + 120)/(x X 5/18)  = 20
x = 54 kmph
T/(54 X 5/18)  = 10, T = 150 meter
So, (180 + 150)  / (54 + 54) X5/18 = 11 sec

9. (a) Let speed of A = x kmph
& speed of B = y kmph & x > y
When they are travelling in same direction, time taken be t
2PiR/ (x – y) = t ……………. (i)
When they are travelling in opposite direction
2PiR/(x + y) = t/4 …………….. (ii)
From Eq (i) & (ii)
x + y /x – y = 4
By C & D
x/y = (4 + 1)/(4 -1)  = 5/3
x : y  = 5 : 3

10. (b) Time taken for the three people meet in hours
= LCM (2/4, 2/6, 2/8)
= 1 hours

All About Time And Distance

Introduction:-

The terms time and distance are related to the speed of a moving object.

Speed: Speed is defined as the distance covered by an object in unit time.

Some Important Facts

Distance travelled is proportional to the speed of the object if the time is kept constant.

Distance travelled is proportional to the time taken if speed of object is kept constant.

Speed is inversely proportional to the time taken if the distance covered is kept constant.

If the ratio of two speeds for same distance is a:b then the ratio of time taken to cover the distance is b:a

Relative Speed 

If two objects are moving in same direction with speeds of x and y then their relative speed is (x – y)

If two objects are moving is opposite direction with speeds of x and y then their relative speed is (x + y)

Unit Conversion

Some Important Shortcut Formulas

Rule 1: If some distance is travelled at x km/hr and the same distance is travelled at y km/hr then the average speed during the whole journey is given by

Example

John goes from his home to school at the speed of 2 km/hr and returns at the speed of 3 km/hr. What is his average speed during whole journey in m/sec?

Sol:

Let’s say x = 2 km/hr

And y = 3 km/hr, so

Now, average speed in m/sec

= 2.4*(5/18) = .67m/sec

Rule 2: If a person travels a certain distance at x km/hr and returns at y km/hr, if the time taken to the whole journey is T hours then the one way distance is given by

Example

Mr Samson goes to market at the speed of 10 km/hr and returns to his home at the speed of 15 km/hr. If he takes 3 hours in all, what is the distance between his home and market?

Sol:

Let’s say x = 10 km/hr

y = 10 km/hr, and

T = 3 hrs, then

So the distance between home and market is 18 km.

Rule 3: If two persons A and B start their journey at the same time from two points P and Q towards each other and after crossing each other they take a and b hours in reaching Q and P respectively, then

Example

Two persons Ram and Lakhan start their journey from two different places towards each other’s place. After crossing  each other, they complete their journey in 1 and 4 hours respectively. Find speed of Lakhan if speed of ram is 20 km/hr.

Sol:

Let’s say A = Ram and B = Lakhan

a = 1 and b = 4, then

(20/Lakhan speed)  = (2/1)

Lakhan’s Speed = 10 km/hr

Rule 4: If the same distance is covered at two different speeds S1 and S2 and the time taken to cover the distance are T1 and T2, then the distance is given by

Example

Two trucks travel the same distance at the speed of 50 kmph and 60 kmph. Find the distance when the distance when the time taken by both trucks has a difference of 1 hour.

Sol:

Let’s say S1 = 50 kmph,

S2 = 60 kmph

T1 – T2 =  1

Distance = [(50*60)/(60-50)]*1 = 300km

Quiz On Time And Distance:-

1.Busses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes?

a.3 km/hr

b.4 km/hr

c.5 km/hr

d.7 km/hr

e.None of these

2.The distance between two cities A and B is 330km. A train starts from A at 8 (a)m. and travels towards B at 60 km/hr. Another train starts from B at 9 (a)m. and travels towards A at 75 km/hr. At what time do they meet?

a.10 am.

b.10 : 30 am.

c.11 am.

d.11 : 30 am.

e.None of these

3.Two trains are moving on two parallel tracks but in opposite directions. A person sitting in the train moving at the speed of 80 km/hr passes the second train in 18 seconds. If the length of the second train is 1000 m, its speed is?

a.100 km/hr

b.120 km/hr

c.140 km/hr

d.150 km/hr

e.None of these

4.In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay’s speed is?

a.5 kmph

b.6 kmph

c.6.25 kmph

d.7.5 kmph

e.None of these

5.It takes eight hours for a 600 km journey, if 120 km is done by train and the rest by car. It takes 20 minutes more, if 200 km is done by train and the rest by car. The ratio of the speed of the train to that of the cars is?

  1. 2 : 3
  2. 3: 2
  3. 3 : 4
  4. 4 : 3
  5. None of theseAnswers with Explanation:-

1.(c)

Distance covered in 10 minutes at 20 kmph = distance covered in 8 minutes at (20+x) kmph

20× 10/60=8/60(20+x)

200 = 160 + 8x

8x = 40

x=40/8=5 kmph

 

2.(c) Distance travelled by first train in one hour

= 60 x 1 = 60 km

Therefore, distance between two train at 9 a.m.

= 330 – 60 = 270 km

Now, Relative speed of two trains = 60 + 75 = 135 km/hr

Time of meeting of two trains =270/135=2 hrs.

Therefore, both the trains will meet at 9 + 2 = 11 A.M.

 

3.(b) Let the speed of second train be x m/s.

80 km/h = (80×5)/18 m/s

According to the question 1000/(x+(80×5)/18)=18

100 – 18x + 400

x=666/18 m/s

= 600/18×18/5 km/h = 120 km/h

 

4.(a)

Let Abhay’s speed be x km/hr.

Then, 30/x-30/2x= 3

6x = 30

x = 5 km/hr.

 

5.(c)

Let the speed of the train be x km/hr and that of the car be y km/hr.

Then, 120/x+480/y= 8        1/x+4/y=1/15 ….(i)

And, 200/x+400/y=25/3      1/x+2/y=1/24 ….(ii)

Solving (i) and (ii), we get: x = 60 and y = 80.

Ratio of speeds = 60 : 80 = 3 : 4.

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