Problem Solving

Hi kasiaw99,

Mitch has provided a great explanation for this question, so I won't rehash any of that work here. Instead, it's worth noting that this question (or something very near to it) WILL show up at least once on Test Day. It's a "classic" in the realm of standardized testing - understanding the concepts of Average Speed and Weighted Averages will be worth points on the GMAT. These questions tend to be "story" problems, so getting all of the information on the pad is KEY - draw pictures, write down formulas, label your work. Do everything necessary to stay organized.

GMAT assassins aren't born, they're made,
Rich

kasiaw99 wrote:I would be grateful for some help answering this question.

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 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!

Solution:

This problem can be solved by using a Rate-Time-Distance table. We are given that Francine traveled x percent of the distance at a rate of 40 mph.

Since we are working with percents, and 100% is the total distance percentage, we can say that (100 - x) percent = the percentage of the remaining distance. Thus, we know that Francine traveled (100 - x) percent of the distance traveled, at a rate of 60 mph.

Since we are working with percents, we can choose a convenient number for the total distance driven; we'll use 100 miles.

Let's fill in the table.



Remember, time = distance/rate, so we use the entries from the chart to set up the times:

Time for x percent of the distance = x/40

Time for (100 - x) percent of the distance = (100 - x)/60

Finally, we must remember that average rate = (total distance)/(total time). Our total distance is 100. The total time is the sum of the two expressions that we developed in the previous steps. Here is the initial setup:

100/[(x/40 + (100 - x)/60)]

Now work with the fractions in the denominator, getting a common denominator so that they can be added:

100/[(3x/120 + (200 - 2x)/120)]

100/[(200 + x)/120)]

This fraction division step requires that we invert and multiply:

100[120/(200 + x)]

12,000/(200 + x)

Answer: E