jscpba 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)
What is the best way to attack this question?
Thanks guys
We can plug in a value for the distance and a value for x.
Let distance = 100 miles.
Let x = 40.
Distance for 40% of the trip = .4*100 = 40 miles.
Since the rate for this portion is 40mph, time = d/r = 40/40 = 1 hour.
Distance for remainder of the trip = 100-40 = 60 miles.
Since the rate for this portion is 60mph, time = d/r = 60/60 = 1 hour.
Total time = 1+1 = 2 hours.
Average speed for the whole trip = (total distance)/(total time) = 100/2 = 50. This is our target.
Now we plug x = 40 into all the answer choices to see which yields our target of 50.
Only answer choice E works:
(12,000)/(x+200) = 12000/(40+200) = 50.
The correct answer is
E.
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