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- HCF and LCM
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# Speed Distance and Time Shortcut and Tricks

## Shortcuts for Speed Time and Distance

### The concept of Speed Time and Distance revolves around these basic formulas:

*To find the solution to speed, distance, and time problems, you can use the following shortcuts:*

To find speed: Speed = \frac{Distance}{Time}. Divide the distance traveled by the time taken to get the speed.

To find distance: Distance = Speed × Time

Multiply speed by the time taken to cover the distance

To find time: Time = \frac{Distance}{Speed}

Divide distance by speed to get the time taken.

These formulas are useful in solving various problems related to speed, distance, and time. But keep in mind to use proper units.

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Type: 1 Shortcut to find Average speed when time is same

Average Speed =\frac{Speed1 + Speed2}{2}

Example:

Musk travels 600 km at 50kmph. He then travels another 700km at 50kmph. What is the average speed?

Solution:

Time taken for 600km = 600/50 = 12 hours

Time taken for 700km = 700/50 = 14 hours

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

S1 = 50

S2 = 50

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

Type: 2 Shortcut to find **Average speed when distances are same**

S_{a}= \frac{2S1 \times S2}{S1 + S2}**Example:**Suraj Ranjhas travels from his house to park at a speed of 70kmph. He suddenly returns home at a speed of 80 kmph. What is his average speed?

**Solution:**

S1 = 70

S2 = 80

Sa = 2(70×80)/(70+80)

= 11200/150

= 74.67 kmph

Type: 3 Shortcut to find time when two trains will meet**The distance between two cities Kanpur and Allahabad is 560 Km. A train starts from Kanpur at 8 a.m. and travel towards Allahabad at 120 km/hr. Another train starts from Allahabad at 9 a.m and travels towards Kanpur 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 Shortcut to find ****Least time to meet in a circular race**

T1, T2, T3 are the Individual times taken by racers to complete one circle respectively .**Example:**Three persons participate in a race which was on a circular track of length 600m. Ram, Rahul and Rajat participated 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

Ram = 600/2 = 300 seconds = T1

Rahul = 600/4 = 150 seconds = T2

Rajat = 600/5 = 120 seconds = T3

LCM(T1, T2, T3) = 600 seconds

Time taken by them to meet at starting point for the first time = 600 seconds.

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- Work and Time – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Boats and Streams – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Pipes and Cisterns – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

- Work and Time –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Boats and Streams –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Pipes and Cisterns –

Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts

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