Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.

To elaborate more: the least time one could complete the race is 20/8=2.5 hours, hence \(S+R\geq{5}\). Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that \(S+B\geq{5}\), so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.

Hope it's clear.
_________________

Given that S+R=B+2, where S, R, and B are times in which Stephanie, Regine, and Brian completed the race.

Min time one could complete the race is 20/8=2.5 hours. Let's see if Brian could have won the race: if he ran at the fastest rate, he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, which is not possible as sum of two must be more than or equal the twice the least time: 2*2.5=5. So Brian could not have won the race.

There is no reason to distinguish Stephanie and Regine so if one could have won the race, another also could. So both could have won the race.

Answer: D.
_________________

The least time one could complete the race is 20/8=2.5 hours, hence \(S+R\geq{5}\). Let's see if Brian could have won the race: best chances to win he would have if he ran at the fastest rate, so he would complete the race in 2.5 hours, so combined time needed for Stephanie and Regine would be S+R=B+2=4.5 hours, but we know that \(S+B\geq{5}\), so even if Brian ran at his fastest rate to win the race, given equation S+R=B+2 can not hold true. Hence Brian could not have won the race.
_________________

We don’t know who has won the race and who has come last. All we know is the fastest time is 2.5 hrs and the fastest speed is 8mi/hr.
Let’s us assume that Brain won the race. He took 2.5 hrs to complete the race. In this case
S + R = 4.5
Now the minimum possible time S and R could have taken would be 2.25 hrs to complete the race, since if they took any time less than 2.25 hrs (which is already less than 2.5hrs), then it would mean that Brian wasn’t the first to win the race.

Note that if S (or R) took more than 2.5 hrs, it means R (or S) took less than 2.5 hrs, and hence Brian wouldn’t be winner in that case.
Now even if they took 2.25 hrs, still the case is not possible, because Brian needs to take the lowest time in order to be winner. So we come to conclusion that Brian cannot be a winner in any case.

Let’s assume that Stephanie won the race in record time of 2.5 hrs. In that case
B = R + 0.5
Note that even if R took the minimum possible time of (2.6 hrs), then Brian would be 3.1 hrs and Stephanie would be 2.5 hrs. This case is very much possible. So S came first, then R and B came last.
The same is true with
B = S + 0.5
R came first, S and then B.
So we see that B is a loser in any case, however R or S have equal chances to win.
So (D) is the answer.

Thanks
Prashant

Can someone clarify this.

1. Stephanie, Regine, and Brian ran a 20 mile race - [D = 20miles]
2. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours - [S + R = B + 2]
3. nobody ran faster than 8 miles per hour - [Max Speed = 20/8 = 2.5m/h]

What if
A. S = 2, R = 1.8 then B = 1.8 so S would win the race.
B. S = 1.8, R = 2 then B = 1.8 so B would win the race.
C. S = 2.1, R = 2.1 then B = 2.2 so B would win the race.

Why not option E? Where am i going wrong?

Isn't this a much easier way to solve this?
I may be wrong:

There are 3 times, Ts Tr and (Ts+Tr-2). Now, we're told that the distance is 20 miles and the max they could have run is 8 m/h.
Let's say Brian beat Stephanie, and we'll start with Brian because Brian has the funkiest time formula. You would have
Ts+Tr-2<Ts, picking Stephanie for no reason, we can do this for Regine as well. You will get Tr<2hours. That means Regine is going 20miles/<2hours, which is >8m/h, which is not allowed. So he cannot beat Regine, and if you just look at the formula you can see he can't beat Stephanie for the same reason. So Brian cannot win. A quick comparison of 20/Ts < 20/Tr will show it is perfectly possible for S to beat R and vice versa.

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________

Hi Bunuel

Why so S+R>=5 ?????

Rgds
Prasannajeet

It's a good conceptual question. Here are my thoughts on it:

8 mph implies that each person took at least 20/8 = 2.5 hrs. They could have taken more time too.
So Stephanie and Regina's combined time is at least 2.5*2 = 5 hrs. So Brian's time taken is at least 3 hrs. Can Brian win? No. The difference between S and R's combined time and Brian's time is 2 hrs but each person takes more than 2.5 hrs.

If S and R together took 5 hrs, B took 3 hrs. Both S and R must have taken 2.5 hrs each.
If S and R together took 6 hrs, B took 4 hrs. Both S and R must have taken less than 4 hrs since each person takes at least 2.5 hrs.
If S and R together took 10 hrs, B took 8 hrs. Both S and R must have taken less than 8 hrs since each person takes at least 2.5 hrs.
Brian could never win.
_________________

We know t1+t2=t3 +2 -- (1)

where t1, t2 and t3 are the time taken by Stephanie, Regine and Brian to complete the race.
Since the minimum value for the time taken is 2.5, t1 or t2 has to be lesser than t3 for equation 1 to hold true. So Brian could not have won the race. But we can find values for t1 and t2 such that stephanie and Regine could have won the race satisfying equation (1).
_________________