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

Описание: In this class Mayank gives a very nice and unique perspective into Races and Head Start Problems.
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
No Head Start
Finish Data
Wining In Time ⇾ Distance Same
Winning by Distance ⇾ Time Same
One Slide for All Problems
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.
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?
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?
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%?
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?
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.
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?
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?


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Mayank Bomb had worked as Sr. Architect with Intel Corporation, Hillsboro, USA. He has 5 Patented Inventions in Computer Architecture. He is a ECE graduate from University of Texas Austin, USA & B. Tech. EE from IIT Varanasi. #examrace #upsc #ugcnet