swimming race

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swimming race

by hemant_rajput » Wed Jan 30, 2013 8:19 am
OK guys, let me make one thing clear that this is not a GMAT question. I know how to solve this question, but all I'm looking for is the best approach to solve it quickly.


Q34 . A and B start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lane and at uniform speeds, but A is faster than B. They first pass at a point 18.5 m from the deep end and having completed one length each one is allowed to rest on the edge for exactly 45 sec. After setting off on the return length , the swimmer pass for the second time just 10.5 m from the shallow end. What is the length of pool?

a. 55.5
b. 45
c. 66
d. 49
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by GMATGuruNY » Wed Jan 30, 2013 10:07 am
hemant_rajput wrote:OK guys, let me make one thing clear that this is not a GMAT question. I know how to solve this question, but all I'm looking for is the best approach to solve it quickly.


Q34 . A and B start a two-length swimming race at the same moment but from opposite ends of the pool. They swim in lane and at uniform speeds, but A is faster than B. They first pass at a point 18.5 m from the deep end and having completed one length each one is allowed to rest on the edge for exactly 45 sec. After setting off on the return length , the swimmer pass for the second time just 10.5 m from the shallow end. What is the length of pool?

a. 55.5
b. 45
c. 66
d. 49
First meeting:

B----18.5----><----------------------------------A

For A and B to meet the first time, they must work together to cover the length of the pool ONCE, as show in the figure above.
Distance traveled by B = 18.5 meters.
The implication:
For each length of pool traveled, B will travel 18.5 meters.


Second meeting:

...........................B----------------------------------->
...............................................................<------10.5--------
<------------A
-------------------------------->

For A and B to meet a second time, the length of the pool must be traveled a TOTAL OF 3 TIMES.
As shown in the figure above:
B must travel one length to the opposite side and then 10.5 meters BACK to meet A.
A must travel one length in the opposite direction and then turn back to meet B.
The result is that the length of the pool is traveled a total of 3 times.
Thus, after the first meeting, TWO MORE LENGTHS of pool are traveled.
Since B travels 18.5 meters for each length traveled, the distance traveled by B after the first meeting = 2(18.5) = 37 meters.

Thus, the TOTAL DISTANCE traveled by B = 18.5 + 37 = 55.5 meters.
As shown in the second figure, the total distance traveled by B is equal to one length of the pool (when B travels to the opposite side) plus 10.5 meters (when B turns back to meet A the second time).
Thus:
55.5 = pool length + 10.5
Pool length = 55.5 - 10.5 = 45.

The correct answer is B
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