Race: A contest of speed over a specified distance is called race.
Eg: Running, Driving, Riding, Sailing, Rowing, etc… are the areas where the Race is concerned.
Race Course: The ground or path on which the races are arranged is called a race course.
- The point from where a race begins is called the starting point.
- The point where the race finishes is called the winning post or finishing point or goal.
- The person who first reaches the goal is the winner.
Dead-heat Race: If all the contestants of a race reach the goal exactly at the same time, then the race is called a dead-heat race.
If P and Q are two contestants in a race, then the following statements and their corresponding meanings are very useful in solving the problems.
|P beats Q by t seconds||P finishes the race t seconds before Q finishes.|
|P gives Q a start of t seconds||P starts t seconds after Q starts from the same point.|
|P gives Q a start of x metres||While P starts at the starting point, Q starts x metres ahead from the starting point at the same time.|
|Game of 100||A game in which the participant scoring 100 points first is the winner.|
|In a game of 100, “P can give Q 20 points”||While P scores 100 points, Q scores only 100 – 20 = 80 points.|
- If P is n times as fast as Q and P gives Q a start of x metres, then the length of the race course, so that both P and Q reach the winning post at the same time must be,
- P can run x m race in t1 seconds and Q in t2 seconds, then P beats Q by a distance
metres [Here t2 > t1]
Suppose A, B, and C participate in a race. The length of the race is L meters. If A is the winner , i.e A gets the first position, in the race.
If A beats B by x meters and A beats C by y meters
◄══════ L ══════════► ◄══════ L ════════════►
X mts y mts
The value of x and y decide will decide the II position in the race.
If x < y then B will beat C, i.e B gets the II position.
If x > y then C will beat B, i.e C gets the II position.
The following rule is used for three participants in a race of same length.
(L – x12 ) x23 = L (x13 – x12 )