Time and Distance is one of the most common and crucial topics covered in any competitive exam’s Mathematics or Quants part. The concept of speed, time, and distance is commonly used in questions about a variety of issues, including straight line motion, circular motion, boats and streams, races, clocks, etc. Aspirants must try to understand the interrelationship of speed, distance, and time.
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What are speed, time, and distance?
Speed: Speed is defined as the rate at which something that is in motion travels a specific distance.
Time: Time is the interval between two events.
Distance: The amount of space between two places.
Time and Distance Formulas |
|
| Speed | $$ \frac{Distance}{ Time} $$ |
| Distance | $$ speed\times time $$ |
| Time | $$ \frac{Distance}{Speed}$$ |
| Average Speed | $$ \frac{Total \ Distance}{ Total\ Time}$$ |
| 1 km/hr | $$ \frac{5}{18}m/sec$$ |
| 1 m/sec | $$ \frac{18}{5}Kmph$$ |
| Assume that somebody travels a particular distance at x km/h and the same distance at y km/h. The average speed for the entire route is | $$ \frac{2xy}{x+y} km/hr $$ |
| If two people, A and B, set off from two points P and Q at the same time and cross paths after spending T1 and T2 hours, respectively, then | $$\frac {A’s\ speed}{B’s\ speed} = \sqrt{\frac {T2}{T1}} $$ |
Note: That speed is directly proportional to distance and inversely proportional to time.
Practice Quizzes
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Time and Distance Quiz 1 – Coming Soon |
Time and Distance Quiz 2 – Coming Soon | Time and Distance Quiz 3 – Coming Soon |
Example problems
Q1. A man travels from Point P to Q with 90 km/hr and from Q to R with 60 km/hr. Total distance between P to R is 200 km. If his average speed is 75 km/hr then find the distance between P and Q?
- 80 km
- 120 km
- 100 km
- 150 km
- None of the given options
Solution:
Q2. A farmer travelled a distance of 61 km in 9 hrs. He travelled partly on foot at the rate of 4 kmph and partly on bicycle at 9 kmph. The distance travelled on foot is:
- 11 km
- 10 km
- 12 km
- 16 km
Solution:
Let, distance travelled on foot = x km.
Then, distance travelled by bicycle =61-x
Then,
x/4 + (61-x)/9 = 9
x/4 – x/9 + 61/9 = 81/9
5x/36 = 20/9
x = 16 km
Q3. A takes 30 minutes more than B to cover a distance of 15 km at a certain speed. But if A doubles his speed, he takes one hour less than B to cover the same distance. What is the speed (in km/h) of B?
- 5
- 13/2
- 6
- 11/2
Solution:
Go through the options, with the help of option C,
The speed of B is 6 km/h.
Time taken by B to cover 15 km = 15/6 = 2 hrs 30 min
Time taken by A to cover 15 km = 2 hrs 30 min + 30 min = 3 hrs
Speed of A = 15/3 = 5 km/h
∴ Time taken by A if A double its speed = 15/10 = 1 hrs 30 min (satisfied)
Q4. The area of a square field is 3600 sq. m. If the speed of a man is 4km/hr then find the time taken by the man to complete a walk along the sides of the field.
- 208 sec
- 213 sec
- 200 sec
- 216 sec
Solution:
Area of a square field = 3600 m2
a2 = 3600 m2
a = √3600
a = 60 m
Perimeter of square field = 4 × a = 4 × 60 = 240 m
The time taken by him to complete a walk along the
sides of the field = Distance/Speed
= 240/4000 × 3600 = 216 sec
Q5. For a certain distance, C takes 60 minutes. The ratio of the speed of A and B is 2 : 1 and the ratio of speed of B and C is 3 :1, so how much time will B take to cover the same distance?
- 20 minutes
- 10 minute
- 60 minutes
- 30 minutes
Solution:
Speed = Distance/ time
Speed ∝ 1/ Time
A : B = 2 : 1
B : C = 3 : 1
Ratio of speed of A : B : C = 6 : 3 : 1
Ratio of time of A : B : C = 1/6 : 1/3 : 1
We can write it as,
A : B : C = 1 : 2 : 6
Time taken by C = 6 = 60 minutes
So, 1 = 10 minutes
It means B = 2 × 10 = 20 minutes
Q6. A man walk at a speed of 4 kmph and a car pass in the same direction, but due to fog a man can see the car only at a distance of 300 m for 4 min. Find the speed of the car.
- 6.5 km/hr
- 7.5 km/hr
- 8.5 km/hr
- 9.5 km/hr
Solution:
Let the speed of the car be x
According to the question,
300 × 18/5 = (x – 4) × 4 × 60
300 × 18/5 = (x – 4) × 240
60 × 18/240 = (x – 4)
9/2 = (x – 4)
4.5 = (x – 4)
x = 4.5 + 4
x = 8.5 km/hr
Q7. How many poles a train crosses when travelling with a speed of 45 kmph in 4 hour. If the distance between two poles is 50 m and poles are counting from starting.
- 1000
- 3601
- 3001
- 1800
Solution:
Distance = Speed × Time = 180 × 1000 = 180000
Total poles passed = {Distance traveled / Distance between poles} + 1
No. of poles = 180000/50 = 3600+1
Total 3601 poles.
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Frequently Asked Questions About Time and Distance
Q. How can I calculate speed?
Speed indicates how rapidly something or someone is traveling. If you know the distance and time it took to go, you can calculate the object’s average speed. Speed is calculated as distance divided by time.
Q. What is speed equivalent to?
The speed represents the pace at which the distance changes over time. If ‘D’ is an object’s distance in time ‘T’, then the speed is s = D/T. It uses the same units as velocity.
Q. What is the SI value for speed?
Meters per second.
The basic unit of speed, or SI unit, is the meter per second. This signifies that it takes one second to cover a one-meter distance.
