On a certain nonstop trip, Marta averaged

jjjinapinch wrote:On a certain nonstop trip, Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours. What was her average speed, in miles per hour, for the entire trip?

(1) 2x + 3y = 280
(2) y = x + 10

Official Guide question
Answer: A

Given: Marta averaged x miles per hour for 2 hours and y miles per hour for the remaining 3 hours

Target question: What was Marta's average speed for the entire trip?
This is a good candidate for rephrasing the target question.
Average speed = (TOTAL distance)/(TOTAL time)
Travelling at x miles per hour for 2 hours, Marta travels a distance of 2x miles
Travelling at y miles per hour for 3 hours, Marta travels a distance of 3y miles
So, the TOTAL distance = 2x + 3y
TOTAL time = 2 hours + 3 hours = 5 hours
So, average speed = (2x + 3y)/5
REPHRASED target question: What is the value of (2x + 3y)/5?

Statement 1: 2x + 3y = 280
Perfect!
This means, (2x + 3y)/5 = 280/5 =56
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: y = x + 10
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 10 and y = 20. In this case, (2x + 3y)/5 = (20 + 60)/5 = 80/5 =16
Case b: x = 30 and y = 40. In this case, (2x + 3y)/5 = (60 + 120)/5 = 180/5 =36
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent