business mathematics

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 starting point and B is ahead
of A by 12 meters. Then we say that "A gives B a start 12 meters.

->To cover a race of 100metres in this case,A will have to cover
100m while B will have to cover 88m=(100-12)

->In a100m race 'A can give B 12m' or 'A can give B a start of
12m' or 'A beats B by 12m'means that while A runs 100m B runs 88m.

Games:
A game of 100m,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'.

Some example 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 7sec 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 3m over B. 3m 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.