Time, Speed And Distance: Notes And Questions

Time, Speed And Distance

Time, speed and distance is an important concept of questions asked in Banking, SSC, CAT and various other competitive exams held every year. While solving the questions, you might get confused on the right formula and tricks to apply to get the answer. In this post, we are going to discuss the important formulas related to Time, speed, distance and relative speed along with examples. The study notes will help you solve the questions related to this topic easily.

Time Speed & Distance Formula 

a) Distance = Time × Speed
b) When Distance is constant


When Time is constant

Distance ∝ speed 

When speed in constant 

Distance ∝ Time 

c) Average speed = (Total Distance )/(Total Time Taken)

When Distance is equal

Average speed= 2xy/(x + y)
x, y → speeds


Time Speed & Distance: Questions 

Q1. A car takes half of the time taken by truck to go from Lucknow to Bombay. A truck takes 20 hours to go for the same journey. What is the speed of truck, if the speed of car be 120 km/hr.

Q2. Shweta when increases her speed from 24 km/hr to 30 km/hr she takes one hour less than the usual time to cover a certain distance. What is the distance usually covered by Shweta?

Q3. Kriplani goes to school at 20 km/hr and reaches the school 4 minutes late. Next time, she goes at 25 km/hr and reaches the school 2 minutes earlier than the scheduled time. What is the distance of her school?

Q4. Udai travels half of his journey by train at the speed of 120 km/hr and rest half by car at 80 km/hr. What is the average speed?

Q5. Walking at 4/5 of his normal speed, Dewang is 15 minutes late in reaching his club. What is the usual time taken by him to cover the distance?

Relative Speed Formula & Questions

(a) When two bodies move in the same direction, Let the speed of two bodies be S_A & S_B. 

Relative speed = S_A – S_B

(b) When two bodies are moving in the opposite direction. Let the speed of two bodies be S_A & S_B.

Relative speed = S_A + S_B.

(c) When two bodies moving towards each other than time taken by them to meet.

D→ Distance between two bodies.
S_A, S_B→ Speed of two bodies.
T, time taken to meet each other = D/(S_A+ S_B )

(d) When two bodies are moving in opposite direction, time taken to meet.

D→ Distance between the two bodies.
S_A, S_B→ Speed of two bodies
T, time taken = D/(S_A  – S_B )

(e) If two persons A & B, start at the same time from P and Q towards each other and after crossing they take T₁ & T₂ hrs in reaching Q & P

S_A/S_B =√(T_B/T_A )

Q1. The distance between 2 places R and S is 42 km. Anita starts from R with a uniform speed of 4 km/hr towards S and at the same time Romita starts from S towards R also with some uniform speed. They meet each other after 6 hours. The speed of Romita is

Q2. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?

Q3. A thief Bhagu Ram is spotted by the policeman Pakad Singh from a distance of 200m. Once they see each other they start Running. What is the distance Bhagu Ram, who is running at 5 km/hr would have covered before being caught by Pakad Singh running at 7 km/hr?

Q4. A train starts from A to B at 9:00 am and takes 6 hours to travel to B. Another train starts from B to A at 10:00 am and takes 8 hours to travel to A. At what time both train will meet?

Q5. Abhinav leaves Mumbai at 6 am and reaches Bangalore at 10 am Praveen leaves Bangalore at 8 am and reaches Mumbai at 11:30 am. At what time do they cross each other?

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