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Time, Speed & Distance # 1

by Gaurav Jain

The concept of time, speed and distance is one of the most important concepts of Algebra and Arithmetic. It is advised to keep yourself prepared to see a question or two from this topic.



This Topic covers following concepts:

-Relationship between time, speed and distance

-Important formulae to solve the related problems

-Average speed and relative speed






TIME: TIME is a component to compare the durations of events and the intervals between them, and to quantify the motions of objects.

SPEED: The speed of a body can be defined as the distance covered by it in Unit time. This statement gives birth to three forumlae.

DISTANCE: The numerical description of "How far two objects are" is called distance. It may also refer to the length between two points that may be present or may get created.





1)

SPEED = \frac{DISTANCE}{TIME}

; Distance is constant%



This also proves SPEED IS PROPORTIONATE WITH \frac{1}{TIME}.
If you notice the distance traveled in a unit time with different speed, greater the speed in a time unit; greater will be the distance covered under that time span.

Example: Mr. X uses his car to go to office which is 50 km from his place.
It takes him 1 hour to reach office if he travels at usual speed of { \frac{50 km}{1 hour}= 50 \frac{km}{hour}}


Suppose, Mr. X on a particular day managed to reach office in 30 mins => \frac{1}{2}hour
We can say that he drove at a higher speed as the distance was constant, 50 km(home to office).


In this case the speed will be\frac{50}{\frac{1}{2}} = 100 \frac{km}{hr}

2)

TIME = \frac{DISTANCE}{SPEED} ; Time is constant


Thus, DISTANCE IS PROPORTIONATE TO SPEED.


Example: Time taken in a particular journey can be changed only in two cases.
Case-1: Change in speed of object -
Case-2: Change in distance covered -

3)

DISTANCE = TIME * SPEED ; Speed is constant


Thus, DISTANCE IS PROPORTIONATE TO TIME.


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
Some conversions related to SPEED are as follows:
To convert kilometer per hour to meter per second: \frac{kilometer}{hour} = \frac{5 meter}{18 second}
To convert meters per second to Kilometer to hour:\frac{meter}{second} = \frac{18 kilometer}{5hour}
To convert kilometer per hour to miles per hour:\frac{kilometer}{hour} = \frac{5 miles}{8 hour}
To convert miles per hour to feet per second:\frac{miles}{hour} = \frac{22 feet}{15 second}





P.T.O.

8 Comments
    Anshul_Goel
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    Anshul GoelFri, 14 Jan 2011 17:25:21 -0000

    i wana do mba how may i prepare for cat and mat

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    gemini555
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    Joydeeo SenguptaThu, 17 Sep 2009 21:14:53 -0000

    Yes this lesson is confusing..also pls show some methods or tricks to solve distance, speed, time problems for the GMAT

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    deepa mittal
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    Deepa MittalTue, 22 Sep 2009 09:34:15 -0000

    You can practice questions in Question bank

    Also, go through the tests in GMAT Community that contains time and distance problems.

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    RIMPLE
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    RIMPLESun, 22 Feb 2009 14:41:06 -0000

    thanks a lot you are doing great job

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    shaya
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    shaya sheenMon, 27 Oct 2008 14:47:28 -0000

    thnx a lot gaurav………….. doing a gr8 job

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    vikrant1986
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    Fri, 24 Oct 2008 15:53:26 -0000

    In point 2 you have mentioned time=speed/distance,isn't time=distance/speed?

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    gauravjain26
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    Gaurav JainMon, 03 Nov 2008 15:41:02 -0000

    You are right Vikrant.

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    gauravjain26
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    Gaurav JainSun, 28 Sep 2008 18:49:07 -0000

    Yes you are correct.Thanks for pointing out

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    Sureshbala
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    SureshSun, 28 Sep 2008 05:52:00 -0000

    Dear Gaurav, look into this…..

    If TIME is constant , SPEED and DISTANCE are directly proportional to each other
    If SPEED is constant, TIME and DISTANCE are directly proportional to each other.

    But, in your lesson you mentioned quite opposite to this.
    Kindly look into this and make the necessary changes in the lesson.

    Regards,

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    magnum
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    MohitFri, 19 Sep 2008 14:39:53 -0000

    When time is constant, with greater speed greater distance will be covered.

    So TIME being constant, DISTANCE is directly proportional to SPEED and not vice-versa as you have stated.

    Also, SPEED being constant, DISTANCE is directly proportional to TIME.

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