# Time,Speed & Distance

Important Formulae:

i) Speed=Distance/Time

ii) Time=Distance/speed

iii) Distance = speed*time

iv) 1kmhr=518ms

v) 1ms=185Kmhr

vi) If the ratio of the speed of A and B is a:b,then the ratio of the time taken by them to cover the same distance is 1a:1b or b:a

vii)  Suppose  a  man  covers  a  distance  at  x  kmph  and  an  equal  distance  at  y kmph, then the AVERAGE SPEED during the whole journey is (2xyx+y) kmph
Out of time, speed and distance we can compute any one of the quantities when we happen to know the other two.

Example: If a car travels along four sides of a square at 100 kmph, 200 kmph, 300 kmph and 400 kmph find its average speed.

Average Speed = Total distance / Total time.

Let each side of square be x km. Then the total distance = 4x km.

The total time is sum of individual times taken to cover each side.

To cover x km at 100 kmph, time  = x / 100.

For the second side time = x / 200.

Using this we can write average speed = 4x / (x/100 + x/200 + x/300 + x/400) = 192 kmph.

Conversion of km/ hr to m/ sec and m/ sec to km/ hr

·       x km/ hr = (x* 5/18) m/sec i.e. just need to multiply 5/18

·       Similarly, x m/sec = (x*18/5) km/sec

Distance is directly proportional to Velocity when time is constant:

Example: A car travels at 30km/hr for the first 2 hrs & then 40km/hr for the next 2hrs. Find the ratio of distance travelled
S1S2=V1V2=34

Example: Two cars leave simultaneously from points A & B (100km apart) & they meet at a point 40 km from A. What is VaVb?
Time is constant so V1V2=S1S2=4060=46

Example: A train meets with an accident and moves at (34)th its original speed. Due to this, it is 20 min late. Find the original time for the journey beyond the point of accident?

Method1: Think about 2 diff. situations, 1st with accident and another w/o accident. As distance in both the cases is constant
So V1V2=T2T1
=>V1[34*V1]=T1+20T1
=> 43=T1+20T1 =>T1=60

Method 2: Velocity decreases by 25% (34 of original speed => decrement by 14) so time will increase by 33.3% (43 of original time => increment by 13)
now, 33.3%=20 min =>100%=60 min

Relative Speed:

Case1: Two bodies are moving in opposite directions at speed V1 & V2 respectively. The relative speed is defined as Vr=V1+V2

Case2: Two bodies are moving in same directions at speed V1 & V2 respectively. The relative speed is defined as Vr=|V1–V2|

Train Problems:

The basic equation in train problem is the same Speed=DistanceTime
The following things need to be kept in mind while solving the train related problems.

• When the train is crossing a moving object, the speed has to be taken as the relative speed of the train with respect to the object.

• The distance to be covered when crossing an object, whenever trains crosses an object will be equal to: Length of the train + Length of the object

Example: If a train traveling at 40 kmph crosses another train of length 100m traveling at 14 kmph in opposite direction in 30 s find the length of the train.

Let length of train be d.

Distance to be covered = d + 100.

Speed = 40 + 14 = 54 kmph = 54 X 5 / 18 = 15 m / s

Time = 30 s.

Distance = speed X time => d+100 = 15 X 30 => d = 350 m.

Boats & Streams:

Let U= Velocity of the boat in still water
V=Velocity of the stream.
While moving in upstream, distance covered, S=(U−V)T
In case of downstream, distance covered ,S=(U+V)T

Example: A man can row 50 km upstream and 72 km downstream in 9 hours. He can also row 70 km upstream and 90 km downstream in 12 hours. Find the rate of current.

Let x and y be the upstream and downstream speed respectively.

Hence, 50/x + 72/y = 9 and 70/x + 90/y = 12
Solving for x and y we get x = 10 km/hr and y = 18 km/hr
We know that Speed of the stream = 1/2 * (downstream speed – upstream speed)
= 1/2 (18 – 10) = 4 km/hr.

Clock:

For clock problems consider the clock as a circular track of 60km.
Min. hand moves at the speed of 60km/hr (think min. hand as a point on the track) and hour hand moves at 5km/hr and second hand at the speed of 3600 km/hr.
Relative speed between HOUR hand and MINUTE hand = 55

 Units Of Measurement: TIME can be measured in: Hours Minutes Seconds Some conversions related to TIME are as follows: 1 Hour = 60 Minutes = 60 X (60 Seconds) = 3600 Seconds
 DISTANCE can be measured in various units. some important are: Miles Kilometers Meters Yards Feet Some conversions related to DISTANCE are as follows: 1 Kilometer = 1000 Meters 1 Kilometer = 0.6214 Miles =1 Mile = 1.609 Kilometer = 8 Kilometer = 5 Miles 1 Yard = 3 feet
 SPEED IS MEASURED IN TERMS OF DISTANCE COVERED / TIME. SOME IMPORTANT UNITS ARE: Miles/hour Kilometers/hour Meters/second