Distance between A and B is 72 miles. Two men started walkin

In such questions, I always look for the symmetrical situation to give me a ballpark figure or at least a range. For example, in many work-rate questions, it helps if you figure out the situation in which the rate of both people is the same.
Here the average speed of A (assuming guy who starts from A is A) is 4 mph and distance is 72 miles. So this means that A would take a total of 72/4 = 18 hours to cover the distance from A to B. If B's speed were also 4, both A and B would travel for 9 hours to meet in the middle.
B has uniform speed per hour so its average will be the simple average of all speeds: 2, 2.5, 3, 3.5, 4, 4.5, ...
4 is actually right in the middle of the 9 speeds and this implies that they both have the same average speed. So they will meet midway between A and B.

Had I obtained that B's average speed is more than 4 then that would tell me that they will meet closer to point A and will take less than 9 hours and so on...

You might feel that in this question it worked because the numbers were such but you will be surprised at the number of times such simple analysis will work because GMAT gives you numbers which fit in place.

They meet after n hours:
4n + [2 + 2.5 + 3 + ........ + {2 + (0.5(n-1)}] + x = 72, where x has to be 0.

Lets try for n = 8:
4(8) + [2 + 2.5 + 3 + 3.5 + 4 + 4.5+ 5 + 5.5] + x = 72
x = 10 ... not correct.

Lets try for n = 9:
4(9) + [2 + 2.5 + 3 + 3.5 + 4 + 4.5+ 5 + 5.5+6] + x = 72
x = 0 .... thats possible.

When they meet after 9 hours, that is mid point.

E.

let t=A's and B's time to meeting
B's ratio of cumulative distance to time=(t+7)/4 mph
4t+(t)(t+7)/4=72
t^2+23t-288=0
(t+32)(t-9)=0
t=9 hours
4t=36 miles distance for A
72-36=36 miles distance for B
they meet midway between A and B

thanks guys
its E
+1 kudos to bth

Can you please help me understand how did you determine 4 as average speed of B from progression 2, 2.5, 3, 3.5, 4 ? We don't know there will be 9 such speeds right. We assumed it to be 9 hours with another assumption as B is also having speed as 4.

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