bblast wrote:hi ,
The question is pretty straight and can be solved by total distance/ total time = avg speed
my whacky brain posted an interesting query on this question. y cant this be treated as a weighted average question ?
20 miles at 50mph------------mean = (20*50)+(20*70) / 40 = 60-----------------20 miles at 70mph
I understand weighted average does not work here as the answer would be clearly 70 as shown above. But why?
sorry if my query is silly.
The problem above requires almost no math.
If you drive x miles at one speed and another x miles at another speed,
the average speed for the entire trip will be just a bit less than the average of the two speeds.
If you go to work at 30 miles per hour and return along the same route at 50 miles per hour, the average speed for the whole trip will be just a bit less than (30+50)/2 = 40 miles per hour.
The reason: more time will be spent traveling at the slower speed, so the average speed for the whole trip will be weighted toward the slower speed.
To illustrate:
Let the distance between home and work = 150 miles.
Time at 30 miles per hour = 150/30 = 5 hours.
Time at 50 miles per hour = 150/50 = 3 hours.
Average speed for the whole trip = 300/8 = 37.5, just a bit less than the average of the two speeds.
A driver completed the first 20 miles of a 40-mile trip at an average speed of 50 miles per hour. At what average speed must the driver complete the remaining 20 miles to achieve an average speed of 60 miles per hour for the entire 40-mile trip? -assume that the driver did not make any stops during the 40 mile trip-
a. 65mph
b. 68mph
c. 70mph
d. 75mph
e. 80mph
We can plug in the answers, which represent the speed for the remaining x miles.
Answer choice C: 70 miles per hour.
The average speed for the whole trip will be just a bit less than (50+70)/2 = 60 miles per hour.
Too slow.
Eliminate A, B and C.
Answer choice E: 80 miles per hour
The average speed for the whole trip will be just a bit less than (50+80)/2 = 65 miles per hour.
Too fast.
Eliminate E.
The correct answer is
D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
