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Divyanshu14
The "quick" methods are easiest to apply using variation when dealing with percentages and ratio. These questions in which you add or subtract fixed values to speed, time etc can be done logically (not using variation) but often require a lot of ingenuity. Is it worth investing yourself to "learn" that ingenuity for GMAT, I am not sure. Perhaps it is better to stick to algebra for these. If the intent is to develop reasoning skills, then yes, it makes sense.
For intellectual purposes, here is how you would do it logically, without equations:
She travels 40 miles in the first hour but realizes that at this speed, she will arrive 1 hour late.
This means that if she maintains this speed, 40 miles of the distance will be leftover by the time she is required to reach.
She increases her speed by 20 miles per hour for the remainder of the trip and arrives 20 minutes early.
So if she travels at speed of 60 mph, she will arrive 20 mins early i.e. she covered the 40 leftover miles and could have covered another 20 miles but doesn't need to. This means she had 3 hrs of time remaining when she switched her speed and a distance of 20 less than 3*60 = 180 i.e. a distance of 160 miles remaining.
How far is the community center from her home?
The center is 40 + 160 = 200 miles away from her home.
Answer (D)
