Technique

Head starts and winning margins in a race

Arithmetic • Time, Speed and Distance • Races

Statement

In a race of length

L

: '

A

gives

B

a start of

s

metres' means

B

runs

L - s

while

A

runs

L

; '

A

beats

B

t

seconds' means

B

's time for his own distance is

t

more than

A

's; and '

A

beats

B

d

metres' means

B

has

d

metres still to run when

A

finishes, so

B

's time for

L - d

equals

A

's time for

L

How to use it

1Write down the distance each runner actually covers before touching any speed.
2A start measured in metres shortens the loser's distance; a beat measured in seconds lengthens the loser's time.
3Convert km/hr to m/s once at the outset so metres and seconds stay consistent throughout.

Worked example

In a

200

m race

P

runs at

8

m/s, gives

Q

a start of

40

m and still beats

Q

5

seconds. What is

Q

's speed?

Step-by-step

1
$P$ runs $200$ m at $8$ m/s, so $P$ 's time is $25$ s
Why: The start given away does not change the winner's own distance.
2
$Q$ runs $200 - 40 = 160$ m in $25 + 5 = 30$ s
Why: The start shortens $Q$ 's distance; the beat lengthens $Q$ 's time.
3
$Q$ 's speed $= \frac{160}{30} = \frac{16}{3}$ m/s

Answer

\frac{16}{3}

m/s

Watch out

A start in metres and a beat in metres look alike and are routinely swapped: the first shortens the loser's distance for the whole race, the second says only where the loser stood at the moment the winner finished.

Builds on

Speed, distance and time

Also known as

gives a start of, beats by seconds, head start in a race, handicap race, start of x metres

Appears in past papers

Statement

Worked example

Appears in past papers

2020 (I)

2018 (II)

2017 (II)