**Time Speed and Distance Tricks Pdf :**

In this section, we are going to see the tricks which are much required to solve train problems.

**Trick 1 :**

If the speed is given in km per hour and we want to convert it in to meter per second, we have to multiply the given speed by 5/18.

**Example :**

90 km/hr = 90 ⋅ 5/18 meters/sec

90 km/hr = 25 meters/sec

**Trick 2 :**

If the speed is given in meter per sec and we want to convert it in to km per hour, we have to multiply the given speed by 18/5.

**Example :**

25 meters/sec = 25 ⋅ 18/5 kms/hr

25 meters/sec = 90 kms/hr

**Trick 3 :**

If the ratio of speeds of two vehicles in the ratio a : b, then the taken ratio of the two vehicles will be b : a.

**Example :**

The ratio of speeds of two vehicles is 2 : 3. Then time taken ratio of the two vehicles to cover the same distance will be 3 : 2.

**Trick 4 :**

If the ratio of speeds of two vehicles in the ratio a : b, then the distance covered ratio in the same amount of time will also be a : b.

**Example :**

The ratio of speeds of two vehicles is 2 : 3.

If each vehicle is given one hour time, then, the distance covered by the two vehicles will be in the ratio 2 : 3.

**Trick 5 :**

If A is twice as fast as B, then the distance covered ratio of A and B in the same amount of time will be 2 : 1.

**Example :**

A is twice as fast as B and each given 1 hour time. If A covers 20 miles of distance in one hour, then B will cover 10 miles of distance in one hour.

**Trick 6 :**

If one increases or decreases the speed of the vehicle in the ratio a : b, then the new speed is

= “b” of the original speed/a

More clearly, new speed is

= (“b” ⋅ original speed) / a

**Example :**

David travels at a speed of 56 miles per hour. If he reduces his speed in the ratio 7 : 6, find his new speed.

New speed = (6 ⋅ 56) / 7

New speed = 48 miles per hour

**Trick 7 :**

If a person covers a particular distance at a speed “a” miles per hour and comes backs to his original position at a speed of “b” miles per hour.

Then the average speed for the total distance covered is

= 2ab / (a + b) miles hour

**Important condition :**

The distance covered in “a” miles per hour and the distance covered in “b” miles per hour must be same.

**Example :**

John travels 300 miles at the speed 45 miles per hour and travels another 300 miles at the speed of 55 miles per hour. Find the average speed for the whole journey.

Average speed for the whole journey is

= (2 ⋅ 45 ⋅ 55) / (45 + 55)

= 4950 / 90

= 55 miles per hour

If you would like to have the shortcuts explained above as pdf document,

If you would like to have practice problems on speed, distance and time,

If you would like to have worksheet on speed, distance and time, please click on the links given below.

**Worksheet on Speed, Distance and Time**

**Worksheet on Speed, Distance and Time - 1**

**Worksheet on Speed, Distance and Time - 2**

**Worksheet on Speed, Distance and Time - 3**

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