sohailmbaprep 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. (180-X)/(2)
b. (x+60)/(4)
c. (300-x)/(5)
d. (600)/(115-x)
e. (12,000)/(x+200)
To make the math easy:
Let x=50%, implying that 50% of the trip is traveled at 40mph, with the other half traveled at 60mph.
Let the distance for each half of the trip = the LCM of 40 and 60 = 120.
Time for the first 1/2 of the trip = d/r = 120/40 = 3.
Time for the second 1/2 of the trip = d/r = 120/60 = 2.
Average speed for the entire trip = (total distance)/(total time) = 240/5 = 48. This is our target.
Now we plug x=50 into the answer choices to see which yields our target of 48.
Only answer choice
E works:
(12,000)/(x+200) = 12000/(50+200) = 48.
The correct answer is
E.
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