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

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

## 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.

## One Slide for All Problems

## Dead Heat ⇾ Same End Point & Same Time

Head Start (with Dead Heat)

In Time ⇾ Distance Same

In Distance ⇾ Time Same

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?

-Mayank