In a race of 4800 meters run on a circular track of 400 meters length

Question

In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5. If they run in the same direction, how many times do they meet in the entire race?

A. 4
B. 5
C. 6
D. 7
E. 8

A. 4 
B. 5 
C. 6 
D. 7 
E. 8

rajatchopra1994 · Accepted Answer

Explanation:

Let the slower athlete speed be 3m/min, the faster = 5m/min

The faster athlete overtakes the slower for first time after 400/2 = 200min i.e. when it has covered 1000 meters. After every 200 minutes Faster athlete will overtake slower athlete

Now the total time taken by Faster athlete to cover entire race = 4800/5 = 960 mins

Hence total no of times he will overtake = 960/200 = 4.8 i.e 4 times

IMO-A

fireagablast · Answer

These questions are a little confusing because i'm not sure what points are supposed to be considered significant.
Does the very start count as a data point? What about the end? Since one guy finishes first, does he "meet" with the other guy after every lap thereafter?

The answer is either 4 (the number of times the faster runner laps the slower runner during the race)
1000M:600M
2000M:1200M
3000M:1800M
4000M:2400M
Or every 2.5 laps:1.5 laps

5 times if you count just the start as significant. 6 if you count just the final end as significant. 
I believe they meet 10 times if you count every lap after the first runner finishes as significant, and that's not an answer choice.

DevangiK · Answer

Let's start by calculating the time through relative speed formula : Relative speed = Relative distance / time
So, here the relative speed is (2) {the difference between ratio of the speed of the two athletes}
Thus, 2=400/T 
T=400/2 = 200 mins

Now, we calculate how much distance will the faster athlete cover in 200 mins => 200 * 5 = 1000 mtrs.

since, it will take 1000 mtrs for the faster athlete to cross the other one in a 4800 mtr race. It becomes quite clear that there will be total of 4 points each after the faster athelete run 1000 mtrs.

The correct ans is option A.

chanyb · Answer

Formula: S = \frac{D }{ T} \frac{S1}{S2}=\frac{3}{5} --> S1 = 3k and S2 = 5k (k >0) D2 = D1 + n x 400 (n>0) Since S2 > S1, there is no way that they can meet within the 1st lap. When the 2 will meet, the time will be the same --> T1 = T2 --> \frac{D1 }{ S1} = \frac{D2 }{ S2} or D1 x S2 = D2 x S1 D1 x 5k = (D1 + 400n) x 3k 5 x D1 = 3 x D1 + 1200n 2 x D1 = 1200n D1=600n D2=1000n for n=5, D2=5000 > 4800. So 0 < n < 5 --> They meet 4 times Answer is A Hope it helps!

ScottTargetTestPrep · Answer

We can let the speed of the faster person = 10 and that of the slower person = 6. Notice that the faster person will finish the race in 4800/10 = 480 seconds.

The faster person must overtake the slower person when he runs exactly 1 lap, 2 laps, etc. more than the slower person. Let t be the time it takes when the faster person overtake the slower person We can create the equations:

10t = 6t + 400 (for 1 lap), 10t = 6t + 800 (for 2 laps), etc.

Notice that none of the values of t can be more than 480 seconds, the time when the faster person finishes his race. Solving the first equation, we have:

4t = 400

t = 100

That is, it takes 100 seconds for the faster person to overtake the slower person by 1 lap.

Solving the second equation, we have:

4t = 800

t = 200

That is, it takes 200 seconds for the faster person to overtake the slower person by 2 laps.

We can see that the values of t are increasing by 100, so it will take 300 seconds for the faster person to overtake the slower person by 3 laps, 400 seconds by 4 laps. Since the next one will be 500 seconds and recall that t can’t be more than 480, then there are only 4 times when the faster person overtakes the slower person.

Answer: A

Bunuel · Answer

TWIN QUESTION: https://gmatclub.com/forum/in-a-race-of ... 14091.html

Kinshook · Answer

Given: In a race of 4800 meters run on a circular track of 400 meters length, the ratio of the speed of the two athletes is 3 : 5.

Asked: If they run in the same direction, how many times do they meet in the entire race?

400 m * 12 laps = 4800 m

Let the speeds be 3x & 5x respectively

When they meet each time
400 = 2x * T
T = 200/x

Time to complete the race = 4800/5x = 960/x

Times they meet = (960/x) / (200/x) = 4.8 ~ 4 times ; Since time they meet should be an integer

IMO A

chetan2u · Answer

A very simple way is :

Let the time taken for each round of 400 m be 5 and 3 respectively for speeds 3:5.

So the time the faster runner takes to finish the race or 12 rounds is  3*12 
In 12*3 time units, the slower would run  \frac{12*3}{5}=7.2  rounds.

As they are running in the same direction, every extra round of faster runner means that he has overtaken the slower once, meaning he met the slower once. 
The lead before faster finishes race is 12-7.2 or 4.8, meaning faster has crossed slower 4 times.

A

MV94 · Answer

Runner 1 runs 3/5 the speed of runner 2. Therefore, he will finish (3/5)*12 laps in the time runner 2 finishes 12 laps. (3/5)*12 >7 but <8, therefore runner 1 is on the 8th lap when runner 2 finishes -> runner 1 has been lapped 4 times.

SHEHAB01 · Answer

Why you consider 4.8 is like 4 times else 5 times?

Posted from my mobile device

KarishmaB · Answer

Responding to a pm:

Race length is 4800 m and track is of 400 m so each runner must run 12 full laps to complete the race.

Ratio of Speeds = 3:5
This means that in the time that the slower person runs 3 laps, the faster one runs 5 laps. When running in the same direction in a circle, two people meet everytime the faster one completes 1 lap more than the slower one. So everytime, the faster one completes 2.5 laps and the slower one completes 1.5 laps, they meet.

So when the faster one completes 5 laps, he has covered 2 laps more than the slower one and hence has met him 2 times. 
In another 5 laps, he will meet the slower onen another 2 times. Now 10 laps of the faster one are done and they have met 4 times.

Once the faster one has completed 12 laps, his race would be over. In the next 2 laps he will not meet the slower one because he meets the slower one after completing 2.5 laps.

Total number of times they met = 4

Answer (A)

iamjatinagrawal · Answer

When I looked at the question and its rating at 805+, I thought this question is so tricky but, its very simple. I have used english words a lot so the solution might seem a little daunting but trust me, it is not. The solution provided below is very simple.

Ratio of speeds is given as 3:5. So let the speeds of A and B be 3x, 5x respectively. Relative speed = 2x (by getting the difference, 5x-3x), since they are running in the same direction.

1 Lap distance = 400, so they would meet for the first time after 400/2x = 200/x.

During this time, the distance covered by A is 600m, B is 1000m. When they meet again, the total distance covered by A and B would be (1200, 2000). If we list out a few more such instances, the pairs would be (from the start of the race):

1st meet - 600, 1000
2nd meet - 1200, 2000
3rd meet - 1800, 3000
4th meet - 2400, 4000

By the time they would have met for the fifth time, B would have crossed the 4800m mark, hence during the race, they will only meet 4 times.

In a race of 4800 meters run on a circular track of 400 meters length

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In a race of 4800 meters run on a circular track of 400 meters length

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