**Time Speed and Distance Shortcuts Pdf :**

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

**Shortcut 1 :**

Let the speed be given in km per hour.

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

**Example :**

108 km/hr = 108 ⋅ 5/18 meters/sec

108 km/hr = 30 meters/sec

**Shortcut 2 :**

Let the speed be given in meter per sec.

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

**Example :**

35 meters/sec = 35 ⋅ 18/5 kms/hr

35 meters/sec = 126 kms/hr

**Shortcut 3 :**

Let the speeds of two vehicles be in the ratio a : b.

Then, the ratio of the time taken by the two vehicles to cover the same distance is b : a.

**Example :**

Let the ratio of speeds of two vehicles be 3 : 4.

Then, the ratio of the time taken by the two vehicles to cover the same distance is 4 : 3.

**Shortcut 4 :**

Let the speeds of two vehicles be in the ratio a : b.

Then, the ratio of distances covered by the two vehicles in the same amount of time is also a : b.

**Example :**

Let the ratio of speeds of two vehicles be 3 : 4. Each vehicle is given one hour time. Then, the distance covered by the two vehicles will be in the ratio 3 : 4.

**Shortcut 5 :**

Let A be twice as fast as B.

Then, the ratio of distances covered by A and B in the same amount of time will be 2 : 1.

**Example :**

Let A be twice as fast as B and each given 1 hour time. If A covers 40 miles of distance, then B will cover 20 miles of distance.

**Shortcut 6 :**

Let the speed of a vehicle be increased or decreased 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 :**

Michael travels at a speed of 63 miles per hour. If he reduces his speed in the ratio 9 : 8, find his new speed.

New speed = (8 ⋅ 63) / 9

New speed = 56 miles per hour

**Shortcut 7 :**

A vehicle covers a particular distance at a speed “a” miles per hour and comes back to its 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 :**

Kevin covers 300 miles at the speed 45 mph and travels another 300 miles at the speed of 55 mph. 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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