swimming race

[hemant_rajput]

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

[GMATGuruNY]

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