Arithmetic Aptitude :: Time and Distance

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Time and Distance Important Formulas


In this article, we will discuss motion formulas and questions of time and distance. Since this subject is an integral part of every competitive exam, you cannot miss this topic. This article will equip you to solve word problems at all times, speed and distance.

1. Speed, Time and Distance:

The unit of distance is kilometers, meters, miles, etc. Generally by using this formula we can find the distance of any running train, car etc.
Speed = \(\left(\frac{Distance}{Time}\right)\)
Time = \(\left(\frac{Distance}{Speed}\right)\)
Distance = \(\left(Speed \times Time \right)\)


2. km/hr to m/sec conversion:

It is always advise to convert the unit given in question as per the options. km/hr. to m/sec. or miles/hr.
km/hr. = \(\left[ x \times \frac{5}{18}\right]\) m/sec.

3. m/sec to km/hr conversion:


m/sec. = \(\left[ x \times \frac{18}{5}\right]\) km/hr.

Note: To remember this above unit conversion (in which just fraction part or getting exchange), you can keep in mind that while converting from big unit (km/hr.) to small unit (m/sec.) [ big -> small] the fraction part should be small (5) to big(18) (big -> small). similar approach you can use while converting m/sec. to km/hr. (i.e [small -> big] the fraction part should be big(18) to small(5)).


4. If the ratio of the speeds of A and B is a : b, then the ratio of the times taken by them to cover the same distance is \(\frac{1}{a}\) : \(\frac{1}{b}\) or b : a.


5. Suppose a man covers a certain distance at x km/hr and an equal distance at y km/hr. then, the average speed during the whole journey is \(\left[\frac{2xy}{(x+y)}\right]\) km/hr.

6. Relative Speed:

Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.