In Mathematics time and distance plays a crucial role and are included as a chapter in class. Speed is mutually related to time and distance. Speed is explained as the concept by which the motion of an object is detected. Speed is interpreted as distance per unit time. Speed, time, and distance can be calculated by the formula when some of the information is given.

For solving questions that relate to chapters or topics like clocks, circular motion, straight line, streams and boats, motion in a straight line, and many more. So, the students should be aware of all the relationships between speed, time, and distance. Speed can be defined as the rate at which an object that is in motion covers a particular distance. The interval that separates two events is known as time and distance is defined as the length of the gap in between the objects.

Speed, Time and distance formula and relation between them

  • Speed = Distance / Time

Speed is inversely proportional to time and is directly corresponding to the distance. This statement means that the speed is equal to the distance covered per unit time.

  • Time = Distance / Speed

Time is oppositely proportional to speed and is directly corresponding to the distance. This statement means that the time is equivalent to the distance covered per unit speed.

  • Distance = Speed X Time

Conversions of Speed, Time, and distance –

The concept of conversion of speed, time, and distance into different units is a very crucial part to solve problem sums. Some of the conversions are discussed below:

  • For changing m/sec to km/hr, one must multiply by 18/5.

Therefore, 1 m/sec = 18/5 km/hr = 3.6 km/hr

  • From changing between km/hour to m/sec, one must multiply by 5/18.

Therefore, 1km/hr = 5/18 m/sec

  • For changing between km/hr to miles/ hr, one must multiply by 5/8.

Therefore, 1km/hr = 5/8 miles/hour

  • For changing between yards to feet, one must multiply by 3.

Therefore, 1 yard = 3 feet

  • For changing between an hour to minutes, one must multiply by 60, and from hours to seconds, one must multiply by 3600.

Therefore, 1 hour = 60 minutes = 60 X 60 seconds = 3600 seconds.

  • For changing between kilometers to meters, one must multiply by 1000.

Therefore, 1 kilometre = 1000 meters = 0.6214 mile

  • For changing between miles to feet, one must multiply by 5280.

Therefore, 1 mile = 5280 feet

  • For converting or changing mile to kilometer, one must multiply it to 1.609.

Therefore, 1 mile = 1.609 kilometre

  • For changing miles to yards, one must multiply it by 1760.

Therefore, 1 mile = 1760 yards.

  • 1 mph = (1 X 1760) / (1 X 3600) = 22/45 yards/sec
  • 1mph = (1X 5280) / (1 X 3600) = 22/15 ft/sec

Time and distance problems

Problem 1

If 14 meters is covered by a man in 1 sec then in 4hours 60 minutes how many kilometers will be covered by him?

  1. 43.2km/s
  2. 53.2 km/sec
  3. 40.8 km/sec
  4. 32.5 km/sec
  5. 50.4 km/sec

Solution: 14 m/sec = 14 X (18/5) k/ph

4 hours 45 minutes = 4 X (3/4)

Therefore, Distance = Speed X Time

= 4 X (18/5) X (12/4)

= 14.4 X 3

= 43.2 km/sec

Problem 2

5:6 is the ratio of the speed between the two trains. If 200 km is run by the second train in 2 hours, then what is the speed of the first train?

  1. 80 km/hr
  2. 78 km/hr
  3. 83 km/hr
  4. 88.5 km/hr
  5. 71 km/hr

Solution: Let the train’s speed be 5x and 6 x km/h=r respectively

Then, 6x = (200/2) = 100

X = (100/6) = 16.6

Therefore, First train’s speed = (5X16.6) km/hr

= 83 km/hr

Problem 3

Suppose a person runs at 50 km/hr instead of 30 km/hr. he might have walked 80 km more. What is the actual distance he runs?

  1. 340 km
  2. 80 km
  3. 156 km
  4. 120 km
  5. 100 km

Solution: Let‘s assume the actual distance run by the man is x km

Then, (x/30) = (x+80)/50

  • 50x = 30x+2400
  • 20x = 2400
  • x = (2400/20)
  • x = 120 km

Conclusion

It is to conclude or solve questions that relate to chapters or topics like clocks, circular motion, straight line, streams and boats, motion in a straight line, and many more. So, the students should be aware of all the relationships between speed, time, and distance. There are formulas related to seed, time, and distance.