Speed, Time and Distance – Basic Concepts, Formulas, Tricks, Aptitude Questions and Solved Examples with Explanation (Video Lessons)

Basics, Formulas and Quick Tricks for Speed, Time and Distance

1. 1 Kmph = (5/18) m/s
2. 1 m/s = (18/5) Kmph
3. Speed(S) = Distance(d) / Time(t)
4. Average Speed = Total distance/Total Time = (d₁+d₂)/(t₁+t₂)
5. When d₁ = d₂, Average Speed = 2S₁S₂/(S₁+S₂), where S₁ and S₂ are the speeds for covering d₁ and d₂ respectively.
6. When t₁ = t₂, Average Speed = (S₁+S₂)/2, where S₁ and S₂ are the speeds during t₁ and t₂ respectively.
7. Relative speed when moving in opposite direction is S₁+S₂
8. Relative speed when moving in same direction is S₁-S₂
9. A person goes certain distance (A to B) at a speed of S₁ kmph and returns back (B to A) at a speed of S₂ kmph. If he takes T hours in all, the distance between A and B is T(S₁S₂/(S₁+S₂)
10. When two trains of lengths l₁ and l₂ respectively travelling at the speeds of S₁ & S₂ respectively cross each other in time t, then the equation is given as S₁+S₂ = (l₁+l₂)/t
11. When a train of length l₁ travelling at a speed of S₁ overtakes another train of length l₂ travelling at speed S₂ in time t, then the equation is given as S₁-S₂ = (l₁+l₂)/t
12. When a train of length l₁ travelling at a speed of S₁ crosses a platform/bridge/tunnel of length l₂ in time t, then the equation is given as S₁ = (l₁+l₂)/t
13. When a train of lengths l travelling at a speed s crosses a pole/pillar/flag post in time t, then the equation is given as s = l/t
14. If two persons A and B start at the same time from two points P and Q towards each other and after crossing they take T₁ and T₂ hours in reaching Q and P respectively, then (A’s speed) / (B’s speed) = √T₂ / √T₁

Questions and Solved Examples on Speed, Time and Distance

Q.1: A man goes from A to B at a speed of 20 kmph and comes back to A at a speed of 30 kmph. Find his average speed for the entire journey?
A. 20 kmph
B. 24 kmph
C. 28 kmph
D. 32 kmph
Answer: B. 24 kmph
Explanation: Distance from A and B be 'd'
Average Speed = total distance / total time
Average Speed = (2d) / [(d/20) + (d/30)]
= (2d) / [5d/60) => 24 kmph

Q.2: Convert the 13/36 m/s into kilometers per hour?
A. 1.2 kmph
B. 1.3 kmph
C. 1.4 kmph
D. 1.5 kmph
Answer: B. 1.3
Explanation: 13/36 m/s = 13/36 * 18/5
= 13/10 = 1.3 kmph

Q.3: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
A. 150 kms
B. 156 kms
C. 162 kms
D. 168 kms
Answer: C. 162 kms
Explanation: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 kms

Q.4: Nikita takes as much time in running 18 meters as a car takes in covering 48 meters. What will be the distance covered by Nikita during the time the car covers 1.6 km?
A. 480 m
B. 520 m
C. 600 m
D. 800 m
Answer: C. 600 m
Explanation: Distance covered by Amar = 18/4.8 (1.6km)
= 3/8(1600) = 600 m


Q.5: By travelling at 40 kmph, a person reaches his destination on time. He covered two-third the total distance in one-third of the total time. What speed should he maintain for the remaining distance to reach his destination on time?
A. 15 kmph
B. 20 kmph
C. 25 kmph
D. 30 kmph
Answer: B. 20 kmph
Explanation: Let the time taken to reach the destination be 3x hours. Total distance = 40 * 3x = 120x km
He covered 2/3 * 120x = 80x km in 1/3 * 3x = x hours
So, the remaining 40x km, he has to cover in 2x hours would be required speed = 40x / 2x = 20 kmph

Q.6: What distance will be covered by a bus moving at 72 kmph in 30 seconds?
A. 450 m
B. 500 m
C. 600 m
D. 750 m
Answer: C. 600 m
Explanation: 72 kmph = 72 * 5/18 = 20 mps
D = Speed * time = 20 * 30 = 600 m

Q.7: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
A. 15 mins
B. 20 mins
C. 25 mins
D. 30 mins
Answer: B. 20 mins
Explanation: Speed Ratio = 1:4 / 5 = 5:4
Time Ratio = 4:51 -------- 5 4 --------- ? => 20

Q.8: Rohit walked 25 meters towards South. Then he turned to his left and walked 20 meters. He then turned to his left and walked 25 meters. He again turned to his right and walked 15 meters. At what distance is he from the starting point and in which direction?
A. 35m East
B. 35m North
C. 40m East
D. 60m East
Answer: A. 35m East
Explanation: Rohit's distance from the starting point A would be:
AE = AD+DE = 20 + 15 = 35m East


Q.9: Sagar was riding bike towards north, turned left road 1 km turns towards left & road 2 kms found himself 1 km west of starting. How far did he road north?
A. 1.5 kms
B. 2 kms
C. 3 kms
D. 3.5 kms
Answer: B. 2 kms
Explanation: He travelled total distance of 3 kms.
From which he travelled 1 km in west.
Hence in all he travelled total 2 kms in north.

Q.10: Walking 7/6 of his usual rate, a boy reaches his school 4 minutes early. Find his usual time to reach the school?
A. 24 mins
B. 26 mins
C. 28 mins
D. 30 mins
Answer: C. 28 mins
Explanation: Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 -------- ? => 28 mins