Hi AAPL,
We're told that A and B ran, at their respective constant rates, a race of 480 m. In the first heat, A gives B a head start of 48 m and beats him by 1/10th of a minute. In the second heat, A gives B a head start of 144 m and is beaten by 1/30th of a minute. We're asked for B's speed in meters/second. This question can be solved in a couple of different ways. Since I don't want to do lots of formulaic math if I can avoid it (since it takes so long), I'm going to use the built-in patterns to save some time.
We're given some comparative data to work with:
1) Each FULL race is 480m
2) When runnner A gives runner B a 48m head start, runner A WINS by 1/10th of a minute (meaning 6 seconds).
3) When runnner A gives runner B a 144m head start, runner A LOSES by 1/30th of a minute (meaning 2 seconds).
We're asked for runner B's speed in meters/second. We can use the DIFFERENCES in distance and time to figure out speed. Since the difference in distances is 144-48 = 96 meters and the difference in times is (6 second WIN) - (2 second LOSS) = 8 seconds, we can figure out B's rate....it's 96/8 = 12 m/sec.
If you're skeptical of this conclusion, then you can use it to verify the speed of Runner A....
In the 1st race...
Running 12m/sec, runner B would run 432m in....
D = (R)(T)
432 = (12)(T)
432/12 = T
36 seconds = T
Since runner A WINS by 6 seconds, runner A needs 30 seconds to complete 480m
D = (R)(T)
480 = (R)(30)
480/30 = R
16 meters/sec = R
In the 2nd race....
Running 12m/sec, runner B would run 336m in....
D = (R)(T)
336 = (12)(T)
336/12 = T
28 seconds = T
Since runner A runs at a constant rate, we know that it takes runner A 30 seconds to run a 480m race. Runner A LOSES by 2 seconds, which "fits" this information (runner B ran 336m in 28 seconds while runner A ran 480m in 30 seconds.....the difference is a 2 second LOSS).
Final Answer: A
GMAT assassins aren't born, they're made,
Rich
