Generally on the GMAT:
When the same distance is traveled at two different speeds, the average speed for the entire trip will be a little closer to the lower speed than to the higher speed.
The reason:
It takes longer to travel the distance at the lower speed than at the higher speed.
Since more time is spent at the lower speed, the average speed for the whole trip will be closer to the lower speed.
vksunder wrote:
During a trip, Francine traveled x percent of the total distance at an average speed of 40 miles per hour and the rest of the distance at an average speed of 60 miles per hour. In terms of x, what was Francine's average speed for the entire trip?
A. \(\frac{(180-x)}{2}\)
B. \(\frac{(x+60)}{4}\)
C. \(\frac{(300-x)}{5}\)
D. \(\frac{600}{(115-x)}\)
E. \(\frac{12,000}{(x+200)}\)
Let x=50%, implying that half the distance is traveled at 40 mph and the other half at 60 mph, with the result that the average speed for the whole trip will be a bit closer to 40 than to 60.
Implication:
When x=50 is plugged into the correct answer, the result will be a bit less than 50.
A. \(\frac{(180-x)}{2} = \frac{180-50}{2} = 65\)
B. \(\frac{(x+60)}{4} = \frac{50+60}{4} = \frac{110}{4} = 27.5\)
C. \(\frac{(300-x)}{5} = \frac{300-50}{5} = \frac{250}{5} = 50\)
D. \(\frac{600}{(115-x)} = \frac{600}{115-50} = \frac{600}{65}\) = less than 10
Eliminate A, B, C and D.
E. \(\frac{12,000}{(x+200)} = \frac{12,000}{50+200} = \frac{12,000}{250} = \frac{1200}{25} = 48\)
Only E yields a value a bit less than 50.
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