Important Facts and Formula:
Races:
A contest of speed in running ,riding,driving,sailing or
rowing is called a Race
Race Course:
The ground or path on which contests are made is called
a race course
Starting Point:
The point from which a race begins is called starting point.
Winning point or goal:
The point set to bound a race is called a winning point.
Dead Heat Race:
If all the persons contesting a race reach the goal exactly
at the same time,then the race is called a dead heat race.
Start:
Suppose A and B are two contestants in a race .If before the
start of the race,A is at the satrtint point and B is ahead
of A by 12 metres. Then we say that "A gives B a start 12 metres.
► To cover a race of 100 meters in this case,A will have to cover
100 m while B will have to cover 88m=(100-12)
► In a 100 m race 'A can give B 12 m or A can give B a start of
12 m or A beats B by 12 m means that while A runs 100 m B runs 88 m.
Games:
A game of 100 m, means that the person among the contestants who
scores 100 points first is the winner.
If A scores 100 points while B scores only 80 points then we say
that 'A can give B 20 points'.
Problems:
1) In a 1 km race,A beats B by 28 m or 7sec.Find A's time over the
course?
Sol: B covers 28 m in 7 sec so,B's time over the course
= 7/28 *1000 =250 sec
A's time over the course =250-7 =243 sec = 4min ,3 sec.
2) A runs 1 3/4 times as fast as B.If A gives B a start of 84 m,how
far must be winning post be so that A and B might reach it at the
same time ?
Sol: Ratio of rates of A:B =7/4 :1 =7 :4 In a game of
7 m A gains 3 m over B. 3 m are gained by A in a race of 7m 84 m are
gained by A in a race of 7*84/3 =196 m Winning post must be 196m
away from the starting point.
3)A can run 1km in 3 min ,10sec and B can cover same distance in
3 min 20 sec. By what distance A beat B?
Sol: clearly A beats B by 10 sec. Distance covered by B in 10 sec =1000/200 *10 =50 m A beats B by 50 meters.
4) In a 100m race,A runs at 8km per hour.If A gives b a start of
4 m and still beats him by 15 sec,what is the speed of B?
Sol: 8000 m -------60*60 sec 100 m ------- 60*60*1000/8000 =45 sec.
Time taken by A to cover 100 m =45 sec.
B covers 100-4 m =96 min 45 sec =60 sec
B's speed =96 *60*60/60*1000 =5.76 km/hr
5) A and B take part in 100m race .A runs at 5km per hour. A gives
B a start of 8 m and still beats him by 8 sec. What is the
speed of B?
Sol : A'speed = 5 km/hr =5*5/18 =25/18 m/s Time taken by A to
cover 100 m =100*18/25 =7.2 sec
Time taken by A to cover 92 m = 72+8 =80 sec
B's speed =92*18/80*5 = 4.14 kmpH.
6) A runs 1 2/3 times as fast as B.If A gives B a start of 80 m,
how far must the winning post be so that A and B might reach if
at the same time?
Sol: Ratio of the speed of A and B =5/3 :1 Thus
in a race of 5 m, A gains 2 m over B 2 m are gained by in a race of
5 m 80 m will be gained by A in a race of 5/2* 80 =200 m
7) A,B and C are three contestans in a kmrace .If A can give B a
start of 40 m and A can give C a start of 64 m,how amny metres
start can b give C?
Sol: A covers 100 m,B covers (1000-40) =960 m C covers 1000-64 m
or 936 m when B covers 960 m,C covers 936 m when B covers 1000 m,
C covers 936*1000/960 m =975 m B can give C a start of 1000-975
or 25 m.
8) In a 100m race,A covers the distance in 36 sec and B in
45 sec.In this race A beats B by?
Sol: Distance covered by B in 9 secs =100*9/45 =20 m A beats
B by 20 m
9) In a 200 m race A beats B by 35m or 7 sec.What is the A's time
over the course?
Sol: B runs 35 m in 7 sec. B covers 200 m in =7*200/35 = 40 sec.
B's time over the course =40 sec
A's time over the course =40-7 =33 sec.
10) In a 300 m race A beats B by 22.5 m or 6 sec.What is the
B's time over the course?
Sol: B runs 22.5 m in 6 sec.
B runs 300 m in =6*300*2/45 =80 sec.
B's time over the course =80 sec.
