Hi All,
This is an old series of posts (most of them are over 10 years old), but 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.
While the prompt doesn't state it, we're meant to assume that the two runners run at constant speeds. 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:
GMAT assassins aren't born, they're made,
Rich
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