If you’ve mastered the STD table method for Time n Work my previous articles, then Average speed is a piece of cake.
Absolutely No need to mugup any formula for average speed.

# Case 1: Distance covered in two phases

Champaklal covers 20 kms at the speed of 15kmph and other  10kms at the speed of 6kmph. What is his average speed throughout this journey?

# Approach #1: Good ol’ STD Table

## Step1: Fill up the Table

 Phase 1 Phase 2 Speed 15 6 Time ?? ?? Distance 20 10

We don’t know how much time he took for each phase but we can find it using STD formula
Speed x time = distance
15 x time = 20
Time for phase1=20/15=4/3

Similarly find the time taken for phase 2 and update the table

 Phase 1 Phase 2 Speed 15 6 Time 4/3 5/3 Distance 20 10

## Important note about STD table:

• While solving Time n Work problems, you can only do addition or subtraction in Speed and distance cells only.
• But for solving average speed you can do only do addition or subtraction in Time and Distance cells only.

## Step2: Addition in last column

Now make a new column and do the addition of phase 1 and 2.

 Phase 1 Phase 2 Total=Phase1+2 Speed 15 6 ?? Time 4/3 5/3 4/3+5/3=9/3=3 Distance 20 10 20+10=30

Run STD formula for last column
Speed x time = distance
Speed x 3 = 30
Speed =30 / 3
Speed =10kmph
Final answer: Champak’s Average speed = 10kmph

# Approach #2: Alligiation method

Average speed is nothing but a “weightage average” and since journey was finished in two phases, we can run the alligiation method.
IF you don’t know the Alligiation (Wine+Water) method, Click ME
Step1 is same here. Fill up all the cells in STD table just like we did in above method.

 Phase 1 Phase 2 Speed 15 6 Time 4/3 5/3 Distance 20 10

Now run the alligiation method (Wine and Water Mixture) using speed as ‘concentration’ and Time as ‘volume”

 Speed (concentration) 6 Average speed m (between 6 to 15) 15 Time (Volume) 5/3 4/3

Run the visual move

# Case 2: Distance covered in three phases

Jethalal travels for 30 minutes @50kmph
For the other 20 minutes, he travels @speed of 30kmph
For the 60 minutes, at the speed of 60kmph.
Find his average speed for this journey.

For STD table to work, Everything must be in same unit, you can see here time is given in minutes but speed is given in kmph. Better convert time into hour.
30 minutes = ½ hour
20 minutes=20/60=1/3 hour
60 minutes= obviously 1 hour!

## Step1: Fill up all cells of STD table

 Phase 1 Phase 2 Phase 3 Speed (kmph) 50 30 60 Time (hr) ½ 1/3 1 Distance

Run STD formula on phase1
Speed x time = distance
50 x ½ =distance
Distance=25 km
Same procedure for phase 2 and 3.
Update the table.

 Phase 1 Phase 2 Phase 3 Speed (kmph) 50 30 60 Time (hr) ½ 1/3 1 Distance 25 10 60

## Step2: Addition in last column

Make a new column for total of Phase 1+2+3
Remember we can only add distance and time but not speed.

 Phase 1 Phase 2 Phase 3 Total Speed (kmph) 50 30 60 ?? Time (hr) ½ 1/3 1 ½+1/3+1=11/6 Distance 25 10 60 25+10+60=95

Run STD fomula on last column
Speed x time = distance
Speed x 11/6=95
Speed =95×6/11=51.81kmph
Final answer: Jethalal’s average speed is 51.81kmph

# Alligiation for three phase?

We can also run alligiation method on three phase journey too but it’ll be too lengthy calculation- anyways here is the ‘direction’:
First run alligiation on phase 1 and 2. You get an avg speed(a)
Now run alligiation on avg speed(a) and Phase 3 and you get final average speed.