Speed, Time & Distance – Concepts and Formula
One of the most prevalent quantitative aptitude topics asked in government tests is speed, time, and distance. This is one of those topics that students are already aware of before they begin studying for competitive exams.
Although the concepts of speed, time, and distance remain the same, the kind of questions presented in exams may vary.
23 word problems related to Speed, Time, and Distance are asked in exams, but candidates may also expect questions about data sufficiency and data interpretation related to Time, Distance, and Speed topic.
So, we are providing you with concepts and formulas of the Speed, Distance, and Time topic to help you prepare properly for the upcoming exams.
When we travel from one point to another, there will be three Quantity that defines this journey – Speed, Distance and Time.
Relation between Speed, Distance and Time.
Distance = Speed X Time
Unit of Speed, distance and time
Speed – km/hr , m/s etc
Time – Seconds(s), Hour (h) etc
Distance – meter(m), kilometre(km) etc
Note : If the distance is in Km then time should be in hr and if the distance is in m(meter) then time should be in s ( second)
How to convert km/hr into m/s
Let’s suppose we want to convert 9 km/hr into m/s
We know that 1km = 1000 m and 1 h = 3600 s
How to convert m/s into km/hr
Let’s suppose we want to convert 10 m/s in km/hr
We know that 1km = 1000 m and 1 h = 3600 s
Question. Convert 18 km/hr into m/s ?
Answer. 18 km/hr = 18 x 5/18 = 5 m/s
Question. Convert 20 m/s into km/hr ?
Answer. 20 m/s = 20 x 18/5 = 72 km/hr
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
Question. Amit takes 21 min to reach his school from his home at the speed of 10 m/s. Next day Amit increases it speed to 15 m/s then how much time he takes to reach the school.
Answer
As distance is same in both the cases , Ratio of speed = 10 : 15 = 2:3
So, the ration of time will be = 3 : 2 ,
so, time take in scond case = 21/3 x 2 = 14 min
Alternate method
Distance between school and home = 21 x 60 x 10 = 12600 m
Time taken in scond case = distance / speed = 12600 / 15 = 840 sec
840 sec = 840/60 = 14 min
Alternate method
When distance is equal, we have T_{1}S_{1 }= T_{2}S_{2}
21 x 10 = T x 15
T = 14 min
Question A person crosses a 600 m long street in 5 minutes. What is his speed in km per hour?
Answer. Speed in m/s = 600/(5 x 60)= 2m/s
Speed in km/hr = 2 x 18/5 = 7.2 km/hr
Question A man covered a distance of 200 km in 4 hours on a bike. How much distance will be covered on a bicycle in 8 hours if he rides the bicycle at onefifth the speed of the bike?
Answer. Speed of bike = 200/4 = 50 km/hr
Speed of bicycle = 50/5 = 10 km/hr
Distance covered = Speed x time = 10 x 8 = 80 km
Question A train leaves Station X at 4.10 P.M. and reaches Station Y at 7.25 P.M. The average speed of the train is 40 km/hr. What is the distance from X to Y?
Answer
Question The speeds of A and B are in the ratio 3 : 4. A takes 20 minutes more than B to reach a destination. In what time does A reach the destination?
Answer Ratio of speed = 3 :4
Ratio of Time = 1/ 3 : 1/4 = 4 : 3
Let A and B take 4x and 3x minutes respectively to reach the destination.
Then, 4x – 3x = 20
x = 20 min,
Time taken by A = 4x = 80 min
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
General formula for Average Speed
Question. Ram travels a distance of 50 km at the speed of 40 km/hr and return with the speed of 10 km/hr. What will be the average speed for whole journey ?
Answer. Wrong way (40 + 10) / 2 = 25 km/hr — X
Correct way
Alternate method
Time (case 1 ) = 50/40 = 1.25
Time (case 2 ) = 50/10 = 5
Question A person wishes to reach his destination 90 km away in 3 hours but for the first half of the journey his speed was 20 km/hr. His average speed for the rest of the journey should be
Answer Time taken to travel first half = 45/20 = 9/4 = 2(1/4) = 2 hr 15 min
Remaining time = 3 hr – 2 hr 15 min = 45 min = ¾ hr
 Problems on ages
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 How to Add and Subtract Fractions
 Percentage Concept
 Mixture and Alligation concepts
 Volume and Surface area – Concepts and Formula
 Profit and Loss – Concepts and Formula
Time Speed and Distance Quiz  Links 
Quiz1  Click Here 
Quiz2  Click Here 
Quiz3  Click Here 
Quiz4  Click Here 
Quiz5  Click Here 
Quiz6  Click Here 
Quiz7  Click Here 
Quiz8  Click Here 
Quiz9  Click Here 
Quiz10  Click Here 
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