__Five Most Important Shortcuts for Time Speed Distance – IBPS RRB/PO /Clerk 2017__

__:__**Formula:**

- Distance = Speed × Time
- Time = Distance/Speed
- Speed = Distance / Time
- Convert Km/h to M/s =Km/h * 5/18 = m/s or m/sec *18/5 = km/h
- Calculate Average Speed = 2xy/x+y
- Two person may walk in same direction or in opposite direction.

**Relative Speed:**

Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. When the two objects are moving in opposite directions, relative speed is computed by adding the two speeds.

**Type: 1**

**Average speed when time is same**

S_{a}= S_{1} +S_{2} /2

**Example:**

A man travels 900 km at 60kmph. He then travels another 600km at 40kmph. What is the average speed?

**Solution:**

Time taken for 400km = 900/60 = 15 hours

Time taken for 600km = 600/40 = 15 hours

Since the time is same in both cases, use the above formula to find out the average speed.

S1 = 60

S2 = 40

Sa = (60+40)/2 = 50kmph

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**Type: 2**

**Average speed when distances are same**

S_{a}= 2(S_{1}S_{2})/ (S_{1}+S_{2})

**Example:**

Sai travels from her house to office at a speed of 70kmph. She suddenly returns home at a speed of 80 kmph. What is her average speed?

**Solution:**

S1 = 70

S2 = 80

Sa = 2(70×80)/(70+80)

= 11200/150

= 74.67 kmph

**Type: 3**

**The distance between two cities A and B is 560 Km. A train starts from A at 8 a.m. and travel towards B at 120 km/hr. Another train starts from B at 9 a.m and travels towards A at 100 Km/hr. At what time do they meet?**

**Solution: **

A started at 8 a.m. and he covered 120 km by the time B started its journey.

Remaining distance = 560-120 = 440 km

Relative speed = 120 + 100 = 220 km/h ( We added both speed as they were running in same direction.

Now they will meet after 440/220 = 2 hours

now they will meet at 9 a.m. + 2 hours = 11 a.m.

**Type: 4**

**Least time to meet in a circular race**

T1, T2, T3, …. = Individual times taken by each racer to complete one circle.

**Example:**

Three persons participate in a race on a circular track of length 400m. They can run at a speed of 2mps, 4mps and 5mps respectively. How long will they take to meet in the starting point for the first time?

**Solution:**

Time taken by each person to complete one circle

Person 1 = 400/2 = 200 seconds = T1

Person 2 = 400/4 = 100 seconds = T2

Person 3 = 400/5 = 80 seconds = T3

LCM(T1, T2, T3) = 400 seconds

Time taken by them to meet at starting point for the first time = 400 seconds.

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**Type: 5**

**Calculate speed of two people moving between two points, A and B, in opposite directions& crossing each other on the way.**

S_{a}/S_{b}=√t_{b}/√t_{a}

**Example:**

Two girls move in opposite directions, one from A to B and other from B to A. The girl from A reaches the destination in 20 hrs and girl from B reaches her destination in 25 hrs, after having met. If former’s speed is 25 km/hr, what will be the speed of latter?

If two bodies A and B move from each other’s starting point in opposite directions, they reach their destinations after having met, then their speeds Sa & Sb are given by,

Where t is the time taken by them to cover the distance.

Sb= (25×20) / 20 = 20 km/hr

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