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.
kasiaw99 wrote:
To answer this question I used the plug-in strategy, and to make it simple I assumed that she travelled at 60 miles/h for 50% of the time. I found the correct answer to be C, however, the book states that it is E.
Any ideas as to what went wrong?
Thanks!
x% represents the percentage not of the total time but of the total DISTANCE.
Let x=50%.
Let the total distance = 240 miles.
Here, 50% of the 240 miles is traveled at 40 miles per hour, while the remaining distance is traveled at 60 miles per hour.
Time to travel 120 miles at a rate of 40 miles per hour = d/r = 120/40 = 3 hours.
Time to travel 120 miles at a rate of 60 miles per hour = d/r = 120/60 = 2 hours.
Total time to travel the entire 240 miles = 3+2 = 5 hours.
Average speed for the entire 240 miles = d/t = 240/5 = 48 miles per hour. This is our target.
Now plug x=50 into the answers to see which yields our target of 48.
Only
E works:
12000/(x+200) = 12000/(50+200) = 12000/250 = 48.
The correct answer is
E.
Note the portion in red above.
Traveling half the DISTANCE at 40 miles per hour does NOT imply traveling for half the TIME at 40 miles per hour.
Since traveling half the distance at 40 miles per hour will take LONGER than traveling the remaining half at 60 miles per hour, the two times will NOT be equal.
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