Race Questions: Simple Time and Distance Diagrams Demystify Head Starts and Dead Heats YouTube Lecture Handouts

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RACES

Image of Races

Image of Races

Image of Races

Speed as Rate

  • Speed = Distance/Time

  • Mind the units

  • Prerequisites:

    • Manipulate speed, distance and time: Watch the class on speed questions.

    • Linear equations in 2 variables: Watch the class on linear equations.

    Image of Speed As Rate

    Image of Speed as Rate

    Image of Speed As Rate

One Slide for All Problems

Image of One Slide For All Problems

Image of One Slide for All Problems

Image of One Slide For All Problems

Image of Institutional Racism In Schools For Races

Image of Institutional Racism in Schools for Races

Image of Institutional Racism In Schools For Races

Dead Heat ⇾ Same End Point & Same Time

Head Start (with Dead Heat)

  • In Time ⇾ Distance Same

  • In Distance ⇾ Time Same

Image of Dead Heat For Same End Point And Same Time

Image of Dead Heat for Same End Point and Same Time

Image of Dead Heat For Same End Point And Same Time

Winning By Distance⇾ Time Remains Same (No Head Start)

No Head Start

Finish Data

  • Wining In Time ⇾ Distance Same

  • Winning by Distance ⇾ Time Same

Time & Distance Diagrams- Most Important

1) in a 2000 M Race between a and B. A Gives B a Start of a Minute but Still Beats Him by 200 M. When He Increases the Head Start to 80 Seconds, the Race Ends in Dead Heat. Find the Speed of A

b = 10 m/s, a = 2000/120 = 16.67

2) a and B Run a Race of 2000 M. First, a Gives B a Head Start of 200 M and Beats Him by 30 S. Next, a Gives B a Head Start of 3 Mins and is Beaten by 1000 M. Find the Time in Minutes in Which a and B Can Run the Race Separately?

b = 20/3 and time = 300 sec = 5 min

A = 25/3 and time = 240 sec = 4 min

3) a Runs 50% Faster Than B. If a Gives a Start of 7 M Race Ends in Dead Heat. What is the Length of the Race?

21 m

4) a’S Speed is 20/19 Times That of B. If a and B Run a Race, What Part of the Length of the Race Should a Give B as a Head Start, So That the Race Ends in a Dead Heat? What if the a Wants to Beat B by 5%? What if the B Wants to Beat a by 10%?

a = 1/20

a = 0

a = 0.145

5) a and B Run a 100 M Race, Where a Beats B by 10 M. To Do a Favour to B, a Starts 10 M Behind the Starting Line in a Second 100 M Race. They Both Run at Their Earlier Speeds. What is the Outcome of Second Race?

1 m

6) in a Kilometer Race, a Beats B by One Minute and B Beats C by 30 Seconds. If a Beats C by 250m in the Same Race. Find the Time Taken by a to Run the Race

270 sec

7) Three Runners a, B and C Run a Race, with Runner a Finishing 12 M Ahead of Runner B and 18 M Ahead of Runner C, While Runner B Finishes 8 M Ahead of Runner C. What Was the Length of the Race?

l = 48 m

Next Circular Tracks

Suppose a and B Are Running a 3 Km Race in a Circular Track of Length 300m. Speeds of a and B Are in the Ratio 4:3. How Often and Where Would the Winner Pass the Other?

Image of Circular Tracks For Races

Image of Circular Tracks for Races

Image of Circular Tracks For Races