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## Time and Distance Formula

Learning the Time and Distance formula is crucial, As Questions based on Time and Distance formula are very common and frequent for school as well as competitive exams. The Time and Distance Formula is frequently utilized in various question types, including motion in a straight line, motion in a circle, boats, streams, races, clocks, etc.

The fundamental ideas of the Time and Distance Formula, are discussed in this article. A few solved examples have also been provided, which will help students the Time and Distance Formula in a better way.

## Time and Distance Formula for Competitive Exams

All the important Time and Distance formulas are given here. Using the Time and Distance formulas you can easily solve the Questions based on Speed Time and Distance.

## Speed Time and Distance Formula List

- Speed = Distance/Time
- Time =Distance/Speed
- Distance = (Speed × Time)
- Average Speed= Total Distance / Total Time
- 1 km/hr = 5/18 m/sec
- 1 m/sec = 18/5 km/hr
- If the ratio of the speeds of A and B is a: b, then the ratio of the times taken by them to cover the same distance is 1/a: 1/b =b: a
- 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 (2xy /x+y) km/hr.
- If two people A and B set out from two points P and Q at the same time and cross paths after spending T1 and T2 hours getting to P and Q, respectively, then (A’s speed) / (B’s speed) equals √(T2 / T1).

## Speed, Time and Distance Formula- **Trains **

The time and Distance formula can be implemented on the problems on Trains. Although the basic concept of Time and distance is the same, some changes are there due to train length. Let’s give a look at the Time and Distance formula for Trains.

1. If the Speed of the two trains is S1 and S2 respectively and lengths are L1 and L2, then,

While moving in the opposite direction | Relative speed = S1+S2 |

Time taken = [(L1 + L2)/( S1+S2)] | |

While moving in the same direction | Relative speed = S1-S2 |

Time taken = [(L1 + L2)/ (S1- S2)] |

2. When two trains of lengths l1 and l2 cross each other at speeds of S1 and S2, respectively, in time t, the equation is given as S1+S2 = (L1+L2)/t.

3. When a train of length L1 passing another train of length l2 passes another train of length L2 at a speed formula is expressed as S1 = (L1+L2)/t

4. when a train of length l1 traveling at a speed of S1 traverses a platform, bridge, or tunnel of length L2 in time t, the equation is stated as S1-S2 = (L1+L2)/t.

5. If the train passes an electric pole than

Length of the Train= Train’s speed × Time
Time = Length of the Train/speed Speed = Length of the Train / Time |

## Speed Time Distance Formula

The formula that relates speed, distance, and time is as follows:

**Speed ($v$) = Distance ($d$) / Time ($t$)**

Where:

- $v$ is the speed or velocity of the object.
- $d$ is the distance traveled.
- $t$ is the time taken to cover that distance.

This formula allows you to calculate the speed of an object if you know the distance it has traveled and the time it took to cover that distance. Similarly, you can rearrange the formula to solve for distance or time if you know the speed and one of the other variables.

Just remember to use consistent units for distance and time in order to get accurate results. If the speed is given in, for example, kilometers per hour (km/h), then the distance and time should also be in compatible units such as kilometers and hours, respectively.

## Distance Formula Speed Time

The distance formula relates to distance, speed (or velocity), and time. It’s commonly used to calculate the distance traveled by an object when you know its speed and the time it has been in motion. The formula is:

**Distance ($d$) = Speed ($v$) × Time ($t$)**

Where:

- $d$ is the distance traveled.
- $v$ is the speed or velocity of the object.
- $t$ is the time the object has been in motion.

This formula assumes constant speed and no changes in direction during the motion. It’s important to ensure that the units of speed and time are consistent when using this formula. If you want to calculate the distance for a segment of motion where the speed changes, you might need to break the motion into segments and calculate the distance for each segment separately.

Remember that speed can be expressed in various units (e.g., meters per second, kilometers per hour, miles per hour), and time can be in seconds, minutes, hours, etc., depending on the context. Always make sure to use the appropriate units to match the problem you are solving.

## Time and Distance Aptitude- Speed Time and Distance Conversions

Here. we have given Some Speed, Time & Distance conversions which are very useful while solving numerical based on the Time and Distance formula.

- 1 kilometer= 1000 meters = 0.6214 mile
- 1 mile= 1.609 kilometer
- 1 hour= 60 minutes= 60*60 seconds= 3600 seconds
- 1 mile = 1760 yards
- 1 yard = 3 feet
- 1 mile = 5280 feet
- 1 km / hour = 5 / 18 m / sec
- 1 m / sec = 18 / 5 km / hour = 3.6 km / hour
- 1 km/hr = 5/8 miles/hour
- 1 yard = 3 feet
- 1 mph = (1 x 1760) / (1 x 3600) = 22/45 yards/sec
- 1 mph = (1 x 5280) / (1 x 3600) = 22/15 ft/sec

## Time and Distance Formula Tricks

We have learned how to calculate speed and time using the fundamental time and distance formula. Let’s now know some tricks to solve Time and Distance problems quickly.

- Speed = Distance/Time
- Time =Distance/Speed
- Distance = (Speed × Time)
- Average Speed= Total Distance / Total Time
- 1 km/hr = 5/18 m/sec
- 1 m/sec = 18/5 km/hr
- If the Speed of the two trains is S1 and S2 respectively and lengths are L1 and L2, then, While moving in the opposite direction 1)Relative speed = S1+S2. Time taken = [(L1 + L2)/( S1+S2)]
- If the Speed of the two trains is S1 and S2 respectively and lengths are L1 and L2, then, While moving in the same direction 1)Relative speed = S1-S2. Time taken = [(L1 + L2)/( S1-S2)]
- If the train passes an electric pole or a man, Speed = Length of the Train / Time
- If two trains of lengths L1 and L2 cross each other at speeds of S1 and S2, respectively, in time t, the equation is given as S1+S2 = (L1+L2)/t.

## Time and Distance Problems by Tricks

Now, Let’s some problems based on Time and Distance formula which will help us to understand the formulas in a good way.

**Q.1. If he runs at a speed of 20Km/hr, how much time does Aditiya take to cover a distance of 400 meters?**

Solution: Aditya’s Speed = 20 km/hr = [ 20 × (5/18)]m/sec = 50/9 m/sec

Time taken to cover 400m = 400 ÷ 50/9 = 400× 9/50 = 72 sec = 1. 2 min.

**Q.2. Rasid travels at a speed of 20 kmph from point A to point B and returns to point A at a speed of 30 kmph. Find his overall journey’s average speed.**

Solution: Assume, Distance between A and B to be “d”

Time is taken to travel point A to B = d/ 20h.

Time is taken to travel from point B to A = d/ 30h.

Total Distance traveled by Rasid = 2d km

Average Speed= Total Distance x Total Time

Or. Average Speed= 2d / [(d/20) + (d/30)]

Or. Average Speed= 2d / [(d/20) + (d/30)]

Or. (2d) / [5d/60] = 24 kmph

**Q.3.A train 100m long is running at the speed of 30 km/h. Find the time taken by it to pass a man standing near the railway line.**

Solution:Speed of the train [ 30 × (5/18)]m/sec = 25/3 m/s.

Distance covered = length of the train = 100m ( because the train crossed a man )

Time taken = [ 100÷(25/3)]=[100× (3/25)]s= 12 sec.(Answer)

## Time and Distance Questions Based on Formula

1. Rafiq cycled 2 km in 12 minutes. reaches a distant station. Find out the speed of the bicycle.

2. A motor vehicle at the same speed travels 217 km in 6 hours and 12 minutes. How much time will it need to go 273 km?

## Time and Distance Formula Problems- Trains

1. A train 1.75 m long travels at 60 km per hour. How much time will the train take to cross a tree?

## Time Speed Distance Aptitude Tricks

When it comes to solving time, speed, and distance problems in aptitude tests, having some tricks and strategies can help you solve them more efficiently. Here are a few tips to consider:

**Use Standard Units:**Make sure to convert all units to a common standard. For example, if speed is given in kilometers per hour (km/h), convert distances to kilometers and times to hours. This helps in avoiding unit conversion errors.**Understand the Formulas:**Familiarize yourself with the basic formulas: Speed = Distance / Time and Distance = Speed × Time. Being comfortable with these formulas can help you set up the problem correctly.**Work with Ratios:**Often, these problems involve ratios between speed, time, and distance. If one of these values is constant, the others will vary inversely. Use this concept to your advantage.**Use Fractions:**Sometimes, fractions can simplify the calculations. For example, if you need to calculate the time taken to cover a certain distance at a given speed, see if any fractions cancel out to simplify the calculation.**Use Visualization:**Draw diagrams or visualize the situation. Drawing a simple line to represent the distance and using arrows to represent the speeds can help you see the relationships more clearly.**Use Approximations:**In some cases, you can use approximations to quickly estimate the answer. For example, if the speed is around 100 km/h and the time is around 2 hours, you can quickly estimate that the distance covered would be roughly 200 km.**Inverse Proportions:**If the speed and time are inversely proportional (one increases while the other decreases), consider using the product of speed and time as a constant to solve problems.**Practice with Sample Problems:**Practice solving a variety of time, speed, and distance problems to build your problem-solving skills and improve your speed.**Plug and Play:**If you’re given multiple values for speed, distance, or time and need to find another value, try plugging the given values into the formula to find the unknown value.**Elimination Technique:**If you’re given answer choices, you can often eliminate unreasonable options based on your understanding of the problem and the given data.

Remember that practice is key. The more you practice these types of problems, the more comfortable and efficient you’ll become at solving them. As you practice, you’ll develop your own preferred strategies and tricks that work best for you.

Time and Distance Formula Questions PDF

Here we have provided the Time and Distance Questions pdf so that students can download and practice that will helps them to remember the Time and Distance formulas. Click on the link provided below.

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