In a 100 metre race, A can allow B to start the race either 10 metres

Question

In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m?

A) 6 m/sec; 18 sec
B) 5 m/s; 18 sec
C) 4 m/s; 15 sec
D) 3 m/s; 12 secs
E) 2 m/s; 6 secs

A) 6 m/sec; 18 sec
B) 5 m/s; 18 sec
C) 4 m/s; 15 sec
D) 3 m/s; 12 secs
E) 2 m/s; 6 secs

Source: 4gmat

Can you tell me different methods through which we can arrive at this answer

Bunuel · Accepted Answer

A can allow B to start the race 10 metres ahead, so the time A need to cover 100 meters equals to the time B needs to cover 90 meters --> 100/a = 90/b, where a and b are the rates of A and B, respectively.

A can allow B to start the race 2 seconds before A, so the time A need to cover 100 meters is 2 seconds less than the time B needs to cover 100 meters --> 100/a + 2 = 100/b.

Subtract one from another: 2 = 100/b - 90/b --> b = 5.

Answer: B.

Or directly: B needs 2 seconds more to cover 100 meters than to cover 90 meters --> 2 = 100/b - 90/b --> b = 5.

Hope it's clear.

ScottTargetTestPrep · Answer

We are given that the distance of the race is 100 meters and that A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finish line at the same time.

Let’s denote the time it takes A to finish 100 meters as t. Then, the speed of A in terms of t is 100/t meters per second. If B can start the race 2 seconds before A and they both finish at the same time, then it takes B t + 2 seconds to finish 100 meters. Therefore, the speed of B in terms of t is 100/(t + 2) meters per second.

Furthermore, we are given that if B starts the race 10 meters ahead of the starting point, then A and B finish at the same time, thus it takes B t seconds to run 100 - 10 = 90 meters. So, the speed of B in terms of t is also equal to 90/t.

Let’s equate the two expressions for the speed of B:

100/(t+2) = 90/t

100t = 90t + 180

10t = 180

t = 18.

So it takes A 18 seconds to finish the 100-meter race. Since B takes 2 seconds longer than A to finish the race, it takes B 18 + 2 = 20 seconds to finish 100 meters, and therefore, the speed of B is:

100/20 = 5 m/s.

Answer: B

sowragu · Answer

In a 100 metre race, A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time. What is the speed of B in m/sec and how long will A take to run 100 m?

A) 6 m/sec; 18 sec
B) 5 m/s; 18 sec
C) 4 m/s; 15 sec
D) 3 m/s; 12 secs
E) 2 m/s; 6 secs

A) 6 m/sec; 18 sec
B) 5 m/s; 18 sec
C) 4 m/s; 15 sec
D) 3 m/s; 12 secs
E) 2 m/s; 6 secs

Straight away we can say .. B travels 10m in 2 sec hence B 's speed is 5m/s .. Only one choice is having 5 m/s.. hence B

jodoubt · Answer

"In a 100 metre race,  A can allow B to start the race either 10 metres ahead of the starting point or 2 seconds before A so that both reach the finishing line at the same time.

So say A has x m/s speed. 
Now if A starts 2s late OR letting B ahead of 10meters. This would amount to the same thing, meaning A being a faster runner would catch up.
So: 
A's speed * 2 s = 10 meters (basically in 2 s time, A would cover up the 10 meters of B's Advantage)
x m/s * 2 s = 10 
therefore x (A s speed) = 5 m/s

gracie · Answer

let b=B's rate
let s=seconds
e1: b*(s+2)=100
e2: b*s=90
subtracting,
b*(s+2)-b*s=10
b=5 ms
100m/5ms=20 secs
A's time=20-2=18 secs
B

Blackbox · Answer

Can someone help me with this question using the Shrinking/Expanding distance approach?

chrtpmdr · Answer

Probably not relevant for you anymore but maybe for other readers, I did it with this approach as well:

Basically the problem does not even need a calculation, because you immediately see that the 2 sec early start will yield to the same outcome as the 10 m + start, which basically means B's speed can only be 5 m/s.

But I was still curious about the second part of the question.

I did it like this:

Gap at the beginning:

10 = r * 20 
0.5 m/s = r

Which is the gap speed, this means A's speed has to be 5.5 m/s 
100 / 5.5 -> 1000 / 55 ~ 18 seconds

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In a 100 metre race, A can allow B to start the race either 10 metres

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In a 100 metre race, A can allow B to start the race either 10 metres

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