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# Time and Distance formula with examples for ssc and bank exams

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Most of the students make mistakes while using time and distance formula in the competitive exams because they don't know the proper way to solve the time and distance questions or equations. These time and distance questions usually asked in ssc and bank exams.

You can learn here easily the correct way to use the time and distance formulas in different-2 questions with examples. After learning you can practice also of time and distance questions and answers for better performance.

Time and distance questions in Hindi also helps to improve your performance in competitive exams.

## Time and Distance Formula for Competitive Exams

What is time time, distance and speed ?

Time

Time is defined as quantity, which governs the order or sequence of an occurrence. In the absence of time, the actual sequence of any occurrence or incident would be lost. If we did not have the concept of time, we would not be able known in what period or in what order something took place.

Unit of time

Hour (h) Second (s) are mostly taken as the unit of time.

Speed

Speed is defined as the distance covered per unit time. It is the rate at which the distance is covered.

Unit of Speed

we commonly take km/h. As unit of speed.

Distance

When an object is moving with a certain speed in a particular time, the displacement made by an object is called the distance.

Unit of distance

Kilometre (km) and metre (m) is usually taken as the unit of distance.

Relation between Time, Speed and distance

The speed of a moving body is the distance travelled by it in time

Hence $$Speed={Distance\over Time}$$

$$Time={Distance\over speed}$$

$$Distacne =(Speed×Time)$$

Important facts and formula

1. km/hr $$= \left(x×{5\over18}\right)m/sec.$$

2. x m/sec  $$= \left(x×{18\over5}\right)km/hr.$$

3. If the ratio of the speed of A and B is a : b, then the ratio of the times taken by them to cover the same distance is  or b:a.

4. 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  km/hr.

Solved Example

Ex.1. How many minutes does Aditya take to cover a distance of 400 m, if he runs at a speed of 20 km/hr ?

Solution:

Aditya’s speed = 20 km/hr $$= \left(20×{5\over18}\right)m/sec={50\over9} mm/sec$$

∴ Time taken to cover 400 m $$= \left(400×{9\over50}\right)sec=72\ sec=1{12\over60} min =1{1\over5}min$$

Ex.2. A cyclist covers a distance of 750 m in 2 min 30 sec. What is the speed in km/hr of the cyclist ?

Solution:

$$Speed = \left({750\over150}\right)m/sec =5m/sec=\left(5×{18\over5}\right)km/hr=18 km/hr$$

Ex.3. A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of a dog are equal to 4 leaps of the hare. Compare their speeds.

Solution:

Let the distance covered in 1 leap of the dog be x and that covered in 1 leap of the hare be y.

$$Then, 3x = 4y → x={4\over 3}y→4x={16\over 3}y$$

∴ Ratio of speeds of dog and hare = Ratio of distance covered by them in the same time.

$$= 4x: 5y={16\over 3}y:5y={16\over 3}:5=16:15$$

Ex.4. An aeroplane flies along the four sides of a square at the speeds of 200, 400, 600 and 800 km/hr. Find the average speed of the plane around the field.

Solution:

Let the side of the square be x km and let the average speed of the plane around the field be y km/hr.

$$Then, {x\over200}+{x\over400}+{x\over600}+{x\over800}={4x\over y}$$

$$↔{25x\over2400}={4x\over y}↔y=\left({2400×4\over25}\right)=384.$$

∴ Average speed = 384 km/hr.

Ex.5. A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the good train in 4 hours. Find the speed of the goods train.

Solution:

Let the speed of the goods train be x kmph.

Distance covered by goods train in 10 hours = Distance covered by express train in 4 hours

∴ 10x = 4×90 or x = 36.

So, speed of goods train = 36 kmph.

Hope these time and distance formulas were useful for you and you can take help from these formulas while solving questions. If you have any problem regarding time and distance formula, you can ask me in the comment section.Please visit on the next page.