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During a trip, Francine traveled x percent of the total dist

Expert replies
by varun289 » Sun Dec 16, 2012 5:26 am
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. (1800 - x) /2
B. (x + 60) /2
C. (300 - x ) / 5
D. 600 / (115 - x )
E. 12,000 / ( x + 200)
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Source: — Problem Solving |

by GMATGuruNY » Sun Dec 16, 2012 5:58 am
varun289 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. (1800 - x) /2
B. (x + 60) /2
C. (300 - x ) / 5
D. 600 / (115 - x )
E. 12,000 / ( x + 200)
Let x=50, so that 50% of the distance is traveled at 40mph and 50% is traveled at 60mph.

When the same distance is traveled at two different speeds, the average speed for the entire trip will be just a bit LESS than the average of the two speeds.
Since (40+60)/2 = 50, the average speed for Francine's entire trip must be just a bit less than 50.

Now plug x=50 into the answers to see which yields an average speed just a bit less than 50.
Only E works:
12,000/(x+200) = 12,000/(50+200) = 48.

The correct answer is E.
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by nisagl750 » Sun Dec 16, 2012 6:48 am
varun289 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. (1800 - x) /2
B. (x + 60) /2
C. (300 - x ) / 5
D. 600 / (115 - x )
E. 12,000 / ( x + 200)
Let the total Distance be 100 Miles.

So, Francine traveled x miles at 40 mph and 100-x miles at 60 mph.
Avg speed = Total dist. traveled/Total time taken.
Total dist. traveled = 100
Total time taken = Time taken to travel (x miles at 40 mph + (100-x)miles at 60 mph)
= x/40 + (100-x)/60
= (60x + 4000 - 40x)/2400
= 4000+20x / 2400
= 200+x / 120

Avg. speed = 100 / (200+x / 120)
= 12000/200+x

Choice E
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by varun289 » Sun Dec 16, 2012 6:50 am
mitch reply is good one , like that
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