[Aptitude] TSD: Average Speed made easy without Formulas (Our Good ol’ STD-Table Method!)

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Pavan Kumar

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.

  1. Case 1: Distance covered in two phases
  2. Case 2: Distance covered in three phases

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 1Phase 2
Speed156
Time????
Distance2010

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 1Phase 2
Speed156
Time4/35/3
Distance2010

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 1Phase 2Total=Phase1+2
Speed156??
Time4/35/34/3+5/3=9/3=3
Distance201020+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 1Phase 2
Speed156
Time4/35/3
Distance2010

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

Speed
(concentration)
6Average speed m
(between 6 to 15)
15
Time
(Volume)
5/34/3

Run the visual move
alligation for avg speed
Answer: average speed =10kmph

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!
Now we are in business.

Step1: Fill up all cells of STD table

Phase 1Phase 2Phase 3
Speed (kmph)503060
Time (hr)½1/31
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 1Phase 2Phase 3
Speed (kmph)503060
Time (hr)½1/31
Distance251060

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 1Phase 2Phase 3Total
Speed (kmph)503060??
Time (hr)½1/31½+1/3+1=11/6
Distance25106025+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.

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18 Comments on “[Aptitude] TSD: Average Speed made easy without Formulas (Our Good ol’ STD-Table Method!)”

  1. Answer for case 2 is
    Final answer: Jethalal’s average speed is 51.818kmph

  2. awesome & really student friendly !!

  3. publish your book.

  4. superb talent I salute u for ur prblm solving approach thanks

  5. very helpful!! thank you sir!!

  6. Sir your methods are really students friendly.Great work

  7. sir
    your method and material is very useful for every person who is preparing for competition as well as me
    please inform me such as useful materials

  8. you r donig good job sir…..thanks

  9. thats graet work keep it up for us

  10. Sir, is 3 months time sufficient for maths, reasoning and GK preparation if my english is already strong?

  11. What is the difference between this and the normal method… just that it’s done in a table. I had to do all the calculations I otherwise would have.

  12. Sir,
    Please can you upload the previous articles, especially the ones which explain the basics for STD & others.

  13. How to solve this using STD method?
    3 pumps, working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

  14. How to solve if the total ( time /distance) are given for both speed ?

  15. Every 15 minutes a train leaves a station and travels at a speed of 36kmph.Agoods train which is coming in the opposite direction crosses these trains in the intervals of 12 minutes .what is th speed of the goods train?
    How to solve these kind of problems?

    1. 45km/hr is that right answer

  16. Sir.
    Your methods is very good to solving the problem.we have to no requirement remember the more formula.thank sir.

  17. Dear Sir,
    I am not able to see the tricky pictures/images which u used to clarify the concept i urge u to get it solve quickly as i am not able to understand the concept .
    Thanks

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