Don’t Average Rates!
Look at the following question:
Sarah goes on a 600-mile trip. She travels at a constant rate of 50
miles per hour for the first 300 miles of the trip, and at a constant rate
of 100 miles per hour for the last 300 miles of the trip. What is Sarah’s
average speed in miles per hour for the entire trip?A (^2003)
B 70
C 75
D 80
E 85
Solution: Many test-takers are tempted to average the rate of 50 and 100
to arrive at an average speed of 75. Though perhaps intuitive, this would
be incorrect. Why? Because Sarah spent more time traveling at a rate of
50 miles per hour than at a rate of 100 miles per hour. Her overall rate
will thus be closer to 50 than to 100. Based on this logic alone, you can
immediately eliminate C, D, and E.
To actually calculate her average speed, you should use the rate formula:
rate = distancetime. The total distance is 600 miles, so you need to calculate the
total time. To determine the total time, you should determine the time
for each part of the trip, and then add these up. Use the r × t = d formula
to determine the time for each part of the trip:
rate (mi/hr) × time (hr) = distance (miles)
↓ ↓ ↓
Par t 1: 50 × x = 300
Part 2: 100 × y = 300
Solve for x:
50 x = 300
x = 6
Solve for y:
100 y = 300
y = 3
The total time is x + y = 6 + 3 = 9. The average speed for the trip is thus
600
9 =
200
3.
The correct answer is Choice A.
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 343
04-GRE-Test-2018_313-462.indd 343 12/05/17 12:04 pm