Time and Distance Part 3 Problem on Races

In this section, we will discuss about problems on RACES which is a prat of time and distance, tips and tricks along with concept and terminologies related to it, and different cases on it.

Races

First, we would learn the language (terminology) of races;

Sr. no.	Term	Meaning
1.	Race	A race is a contest of speed in running, driving, riding, sailing or rowing.
2.	Race Course	The ground/path on which a contest is organized in a systematic way.
3.	Starting Point	The exact point/place from where a race begins
4.	Finishing (Winning) Point	The exact point/place where a race end.
5.	Dead Heat Race	A race in which all the contestants reach the finishing point exactly at the same time.
6.	Head start (Start-up)	A runner allows another runner to stay ahead at the start.

Basic problems on Races

E.g. In a race of 100 m, A gives B a start of 10 m. What distance will be covered by B?

As ‘A’ gives a start to ‘B’ of 10 m

At the start of the race, ‘B’ would be ahead of ‘A’ by 10 m

⇒ 100 – 10 = 90 m distance would be covered by ‘B’(Ans.)

E.g. P covers 1 km in 4 min 30 s, while Q covers the same distance in 5 min. by what distance does P defeat Q?

As P covers distance faster so he would be the winner.

The extra time is taken by Q = 30 s

Distance = (1000/300) × 30 = 100 m (Ans.)

E.g. P can run 1 km in 4 min 40 s, Q can run the same distance in 5 min. How many meters start, can P give to Q in 1 km race, so that the race may end in a dead heat?

As P takes lesser time to cover he would give a start, so as we know in dead heat both crossed the finish line at the same time.

Q runs extra 20 s

Q runs in 300 seconds = 1000 m

Q runs in 1 second = 1000/300 = 10/3 m

Q runs in 20 seconds = (10/3) × 20 = 66.67 m (Ans.)

Note: In a game of x points, A scores x points and in this game, B scores y points. In that game A can give (x – y) points to B where x > y.

E.g. In a game of 100 points, A scores 100 points, while B scores only 75 points. In this game, how many points can A give to B?

A has excessive points which are 100 – 75 = 25 points, so he can give 25 points. (Ans.)

There are very fewer chances of these types of questions to be asked in paper.

WHEN 3 CONTESTANT IN A RACE:

Let A, B & C participate in a race where A wins by beating B by x₁₂ m and C by x₁₃ m.

In this condition

(L – x₁₂) x₂₃ = L (x₁₃ – x₁₂)

Where

L = Length of race course

x₁₂ = A beats B by distance

x₂₃ = B beats C by distance

x₁₃ = A beats C by distance

This is a very useful formula for questions related to races.

E.g.  In a race of 100 m, A beats B by 4 m and beats C by 2 m, by how many meters would A beats C in a 100 m race?

Here Ist is A, IInd is C and IIIrd is B.

L = 100 m

x₁₂ = 2

x₁₃ = 4

x₂₃ = ?

By substituting the values in the formula

 ⇒ (L – x₁₂) x₂₃ = L (x₁₃ – x₁₂)

⇒  (100 – 2 ) × x₂₃ = 100 (4 – 2 )

⇒ 98 × x₂₃ = 200

⇒  x₂₃ = 200/98 = 2.04 m (Ans.)

E.g. A, B, and C are three contestants in a 1 km race. If A can give B a start of 40 m and A can give C a start of 64 m, how many meters start can B give C?

 When A completes 1000 m  in a race B would cover (1000 – 40 = 960 m) and similarly, C would cover (1000 – 64 = 936m).

We got when B covers 960m then C covers 936 m So the distance covered by C when B covers 1000 m distance,

936 /960 × 1000 = 975 m.

So B can give a start of  1000 – 75 = 25 m. (Ans.)

Related Posts

1. Time and Distance Part 1 – https://www.rankershubindia.com/speed-distance-and-time-part-1/

2. Time and Distance Part 2 – https://www.rankershubindia.com/speed-distance-and-time-part-2/

3. Time and Distance Part 4 – https://www.rankershubindia.com/speed-time-and-distance-part-4/

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