### Chapter: Time And Distance

Important formulae and tricks and short cuts of Time and Distance:

We are providing you Important Concepts and Tricks on Speed, Distance & Time which are usually asked in almost all competitive exams like IBPS, Govt. Exams and CAT and in quantitative aptitude of MNCs. Use these below given tricks to solve questions within minimum time. These tricks will be very helpful for your upcoming Competitive Exam.

Important formulae and tricks of Time and Distance:

Speed is a very basic concept in motion which is all about how fast or slow any object moves. We define speed as distance divided by time.
Distance is directly proportional to Velocity when time is constant.

Average Speed Formula:

Average speed =Total Distance covered/ Total Time Taken

When the distance is constant Average speed = 2xy/x+y Where, x and y are the two speeds at which the same distance has been covered.

When time taken is constant Average speed = (x + y)/2 Where, x and y are the two speeds at which we traveled for the same time.

Time and Distance Formula

Distance = Speed × Time. Using this formula, all basic problems can be handled. However, you need to make sure about the correct usage of units while using the above formulas.

Speed is inversely proportional to time taken when distance travelled is constant. So when speed increases, time decreases and vice versa.

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.

• If two objects are moving in same direction with speeds a and b then their relative speed is |a-b|
• If two objects are moving is opposite direction with speeds a and b then their relative speed is (a+b)

Convert from kph (km/h) to mps(m/sec)
For converting kph(kilometre per hour) to mps(meter per second) we use following formula

x km/hr=(x∗5/18) m/sec

Convert from mps(m/sec) to kph(km/h)
For converting mps(meter per second) to kph(kilometre per hour) we use following formula

x m/sec= X *(18/5)  km/h

Distance Constant:

If distance travelled for each part of the journey, ie d1=d2=d3=...=dn=d, then average speed of the object is Harmonic Mean of speeds.

Let each distance be covered with speeds s1,s2,...sn in t1,t2,...tn times respectively.
Then t1 =d/s1
t2 = d/s2
tn =d/sn

then, Average Speed=   [(d + d + d+ ... ntimes)]/ [d/s1 + d/s2+ d/s3+ ... d/sn

Average Speed= (n)/[(1/s1  + 1/s2+ .... 1/sn)]

Time Constant:

If time taken to travel each part of the journey, ie t1=t2=t3=…tn=t, then average speed of the object is Arithmetic

Let distance of parts of the journey be d1,d2,d3,...dn and let them be covered with speed s1,s2,s3,...sn respectively.
Then d1=s1 t ,  d2=s2t, d3=s3t, ... dn=snt

then ,  Average Speed= [(s1/t+ s2/t+ .... sn/t)/(t + t+ ...  ntimes)]

Average Speed=( s1+ s2+s3+ ... + sn)/n

For solved problems on above formulas please visit below sections: