Race Problem - Need Help

Hi,

In the first scenario, A finished less than B 1/10th of a minute or 6 seconds. And A gives B a head start of 48m ( If I do not misunderstand : A would start after B had run 48m).
In the second scenario, A finished more than B 1/30th of a minute or 2 seconds. And A gives B a head start of 144m.

As the time for A to finish the distance of 480 for the two scenarios is unchanged.
The distance left B need to move in the first scenario when A start : 480 - 48 = 432
The distance left B need to move in the first scenario when A start : 480 - 144= 336
Discrepancy in distances B moved of the two cases : 432 - 336 = 96
Discrepancy in times : 6 + 2 = 8. As in 1st case, A is less than B 6 seconds, -- in 2nd case, A is more than B 2 seconds.
Thus between the two cases, B time's discrepancy is 8 seconds.

Speed of B is : 96 / 8 = 12m/s

So pick A.

I didnt understand the discrepancy part

limestone wrote:Hi,

In the first scenario, A finished less than B 1/10th of a minute or 6 seconds. And A gives B a head start of 48m ( If I do not misunderstand : A would start after B had run 48m).
In the second scenario, A finished more than B 1/30th of a minute or 2 seconds. And A gives B a head start of 144m.

As the time for A to finish the distance of 480 for the two scenarios is unchanged.
The distance left B need to move in the first scenario when A start : 480 - 48 = 432
The distance left B need to move in the first scenario when A start : 480 - 144= 336
Discrepancy in distances B moved of the two cases : 432 - 336 = 96
Discrepancy in times : 6 + 2 = 8. As in 1st case, A is less than B 6 seconds, -- in 2nd case, A is more than B 2 seconds.
Thus between the two cases, B time's discrepancy is 8 seconds.

Speed of B is : 96 / 8 = 12m/s

So pick A.

Let's take the point of time when A started to be the initial point of time. The time for A to move 480m is X

From that point of time:

In 1st case: B had moved 480 - 48 = 432m in a period of time : X + 6 ( A beats B 1/10 minutes, or time of B is 6 seconds more than that of A)
In 2nd case: B had move 480 - 144 = 336m in a period of time : X- 2 ( A is beaten 1/30 minutes, or time of B is 2 seconds less than that of A)

Now, we have:

B moved 432m in (X+6) seconds
B moved 336m in (X-2) seconds.
Then it took B more (X+6) - (X-2) seconds to move more (432 - 336)m
Or it took B more 8 seconds to move more 96m
So the speed of B must be: 96/8 = 12m/second

Hope it helps.