26.
RACES AND GAMES
IMPORTANT
FACTS
Races: A
contest of speed in running, riding, driving, sailing or rowing is called 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 known as
a starting point.
Winning Point or Goal: The point set to bound a race
is called a winning paint or a
goal.
Winner: The
person who first reaches the winning point is called a winner.
Dead Heat Race: If all the persons contesting a race reach the goal exactly at the same time, then the race is said to be
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 starting
point and B is ahead of A by 12 metres, then we say that 'A gives
B, a start of 12 metres. '
To cover a race
of 100 metres in this case, A will have to cover 100 metres while B will
have
to cover only (100 - 12) = 88 metres. i
In a 100 m race, 'A can give B 12 m' or 'A can give B a start of 12 m' or 'A beats 12 m' means that while A runs 100 m, B runs
(100 - 12) = 88 m.
Games: 'A
game of 100, means that the person among the contestants who scores 100m 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.
SOLVED
EXAMPLES :
Ex.
1. In a km race, A beats B by 28 metres or 7 seconds. Find A's
time over the course.
Sol. Clearly, B covers 28 m in 7 seconds.
:. B's time over the course = (278 x 1000) sec = 250 seconds.
:. A's time over the
course = (250 - 7-) sec = 243 sec = 4 min. 3 sec.
Ex. 2. A runs 1 ¾ times
as fast as B. if A gives B a start
of 84 m, bow far must
winning post be so that A and B might reach it at
the same time?
Sol. Ratio of the rates of A and B = 7/4 :
1 = 7 : 4.
So, in a race of 7 m, A
gains 3m over B.
:. 3 m are gained by A in a
race of 7 m.
:. 84 m are gained by A in a race of (7/3 x 84) m = 196 m.
:. Winning post
must be 196 m away from the starting point.
Ex.
3. A can run 1 km in 3 min. 10 sec. and B can
cover the same distance in 3 min. 20 sec. By what distance can A beat B ?
Soln:Clearly, A beats B by 10 sec.
Distance covered by B in 10
sec. = (1000 x 10 )m = 50 m.
200
Therefore A beats B by 50 metres.
Ex .4 . In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m
and still him by 15 seconds, what is the speed of B ?
Sol: Time taken by A to cover 100 m =(60 X 60 / 8000) x 100 sec = 45 sec.
B covers (100 - 4) m = 96
m in
(45 + 15) sec = 60 sec.
B's speed = (96 x 60 x 60 )km/hr = 5.76 km/hr.
60 x 1000
Ex.
5. A, Band C are
three contestants in a km race.
If A can give B a start of
40 m
and A can give C a start of 64m how
many metre's start can B give C ?
Sol: While A covers 1000 m, B covers (1000 - 40) m
= 960 m and
C covers (1000 - 64) m or 936 m.
When B covers 960 m, C covers 936 m.
Ex 6. In
a game of 80 points; A can give B 5 points
and C 15 points. Then how many points B can
give C in a game of 60 ?
Sol. A: B = 80 : 75, A : C = 80 : 65.
B/C = ( B/ A *
A/C) = (75 / 80 * 80 / 65) = 15/13 = 60 /52 = 60: 5
Therfore
,In a game of 60, B can give C 8 points.
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