CAT 2022 : RACES & CIRCULAR TRACKS

Now let us discuss the cases of races. Let there be two persons A and B running a race. Sometimes, we deal with the statements like A gives B a start of ‘x’ meter in a race. Now what does it mean? Let us try to find it out.

If we have a statement that A can give B a start of say 10 m in a 100 m race, then it means that when A has covered 100 m then B has covered only 90 m or time taken by A to cover 100 m is same as taken by B to cover 90 m.

The above statement can also be given in terms of time like “In a 100 m race A can give B a start of 5 seconds”. Now it means that the time taken by B to cover the race is 5 seconds more than the time taken by A.

Now let us try some examples based on above statements.

Example 1: In one km race,A beats B by 36 m or 9 sec.Find A’s time to complete the race.

Solution: Here A beats B by 36m. It means that when A has completed the race, B is still 36 m behind, or he has covered 964 m.

In the second part of the statement, it is given that A beats B by 9 seconds. It means that B will take 9 seconds more than A to complete the race.

Now if we join both the parts, we can say that B is still 36 meter behind the finish line, and he will take 9 seconds to complete it. So, the speed of B = 36/9 = 4m/s

So, B will complete the race in 1000/4 = 250 sec and A will take 9 seconds less than B so A will complete it in 241 seconds.

Example 2: P can run a kilometer in 4 minutes and Q in 4 minutes 10 s. By what distance can P beat Q?

Solution: Here we must find the distances covered by P and Q at the same time.

It is given that P completes the race in 4 minutes or 240 seconds and Q completes it in 250 seconds.

Since P is the fast runner and he completes the race in 240 seconds, we will find how many meters Q has run in 240 seconds.

Now in 250 seconds, Q runs 1000 m.

So, in 240 seconds he will run

So, Q has run only 960 m in the time in which P has run 1000m. So, P can beat Q by 1000 – 960 = 40 m.

Example 3: In a 100m race,A runs at a speed of 5m/s.If A gives B a start of 2 m and still beats him by 10 seconds, Find the speed of B.

Solution: Time taken by A to complete the race =

As A beats B by 10s

B will take 10 more seconds than A to complete the race. So, B will take 30 seconds.

B has a start of 2 m, so he must cover 98 m.

So, speed of B =

Example 4: A can run 440 m in 42s and B in 44s. By how many seconds will B win If he had 30 meters start?

Solution: B runs 440 m in 44s.

B runs (440-30)m in

A runs 440m in 42 s

So, B wins by 42 – 41 = 1 sec.

Example 5: In a km race A can beat B by80 m and B can beat C by 60 m. In the same race, by how many meters can A beat C?

Solution: While A runs 1000 m, B runs 1000-80 =920m

And while B runs 1000m,C runs 1000- 60 =940m

When B runs 920 m, C runs =

While A runs 1000m C runs 4324/5 m

A beats C by 1000-4324/5=676/5=

Circular Races

Let us consider that two persons X and Y who are running around a circular track. Let us say that the speed of X is greater than that of Y. Now when the race starts, X will overtake Y. Now after covering some rounds X will catch Y again. Now when X will catch Y again, then X would have covered one circular round more than that of Y.

Now, we come across three types of questions in circular races.

1. After what time will they meet on the track for the first time?
2. After what time will they meet at the starting point?
3. How many points are there on the track including the starting point where they will meet?

We can answer the above questions by using the following table.

If length of circular track is ‘x’ and speeds of the two persons say X and Y are ‘p’ and ‘q’ respectively such that p > q.

	When the two persons are running in same direction	When the two persons are running in opposite direction
Time taken to meet for the first time ever on the track
Time taken to meet for the first time at the starting point	LCM of { }	LCM of { }

The total number of points where they will meet including the starting point =

Now consider that there are three persons X, Y and Z running around the circular track of length ‘x’ and their speeds are p,q,r respectively such that p > q > r.

	When they all are running in same direction	When the two persons say X and Y are running in one direction and Z is running in opposite direction
Time taken to meet for the first time ever on the track	LCM of { , }	LCM of { , }
Time taken to meet for the first time at the starting point	LCM of { , }	LCM of { , }

The total number of points where they will meet including the starting point =

Solve the exercise given below to get a stronger hold on races.

EXERCISE

Question 1: In a circular race along a track of length of 3600m,A and B start from the same point and at the same time with speeds 36 km/h and 45km/h.Find when they will meet for the first time on the track when they are running

1. In the same direction
2. In the opposite direction

Question 2: P,Q, and R run along a circular track 3600m long at speeds of 18 km/h, 27 km/h, and 36km/h.If they start at the same time and in the same direction, when will they meet again at the starting point?

Speed Time Distance Questions: Problems on Speed Time Distance you should solve for competitive examination preparation

Welcome to this exercise on races. In this exercise, we build on the basic concepts for Speed Time Distance and focus onraces. As you prepare for your competitive examinations, you will come across questions on Speed Time Distance with focus on races. Such questions based on races need optimized tackling and can be solved with ease by using simple tricks and understanding the relationships highlighted in this Speed Time DistanceQuestions article. The Speed Time Distance Questions exercise comes into the picture where it gives you a chance to practice the highlighted and important concepts related to this Speed Time Distanceand races question type.