**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**

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

You can also visit our following web pages on different stuff in math.

**WORD PROBLEMS**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**