bacali wrote:Q17:
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. 65 mph
B. 68 mph
C. 70 mph
D. 75 mph
E. 80 mph
First, a quick guessing tip on round trip questions (i.e. any distance question that has 2 parts of equal distance): the average speed will always be closer to the slower of the two speeds.
On this question, we know that 60, the overall average, has to be closer to 50 than to the quick speed. Therefore, the quick speed MUST be greater than 70mph... eliminate (A), (B) and (C). Worse case, we have a 50/50 shot at the question (in under 20 seconds).
Now that we have it narrowed down, let's backsolve!
Plugging in (E) 80:
Part 1:
d = r*t
20 = 50t
t = 2/5
Part 2:
d = r*t
20 = 80t
t = 1/4
Total trip:
d = r*t
40 = r*(1/4 + 2/5)
40 = r(5/20 + 8/20)
40 = r(13/20)
40(20/13) = r
well, 800/13 certainly doesn't equal 60 - eliminate (E), choose (D).
If we had plugged in (D) 75:
Part 1:
d = r*t
20 = 50t
t = 2/5
Part 2:
d = r*t
20 = 75t
t = 4/15
Total trip:
d = r*t
40 = r*(4/15 + 2/5)
40 = r(4/15 + 6/15)
40 = r(10/15)
40 = r(2/3)
40(3/2) = r
60 = r... bingo!
Of course, if you're an algebra person, you could have set up the equations and solved them instead. As a general rule, if the equations jump out at you, algebra is probably your best approach. If the equations don't jump out at you (or if you're a variablephobe), then backsolving is a great alternative.
