deepakrobi wrote:
Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Did Reiko travel from A to B at a speed greater than 40 miles per hour?
(1) Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour.
(2) It took Reiko 20 more minutes to drive from A to B than to make the return trip.
Given: Reiko drove from point A to point B at a constant speed, and then returned to A along the same route at a different constant speed. Target question: Did Reiko travel from A to B at a speed greater than 40 miles per hour?This is a good candidate for
rephrasing the target question.
Let d = the DISTANCE from A to B
Let t = the TIME to travel from A to B
Let u = the TIME to travel from B to A
Speed = distance/timeSo, Reiko's speed from A to B =
d/tREPHRASED target question: Is d/t < 40?Aside: the video below has tips on rephrasing the target question Statement 1: Reiko's average speed for the entire round trip, excluding the time spent at point B, was 80 miles per hour. Average speed = (TOTAL distance traveled)/(TOTAL travel time)We know that the TOTAL distance traveled = d + d = 2d
The TOTAL travel time = t + u
So, when we plug in the values to get:
2d/(t + u) = 80Multiply both sides of the equation by (t + u) to get: 2d = 80t + 80u
Divide both sides of the equation by 2 to get:
d = 40t + 40uNow take the REPHRASED target question,
Is d/t < 40?, and replace d to get:
Is (40t + 40u)/t < 40?Rewrite as:
Is 40t/t + 40u/t < 40?Simplify:
Is 40 + 40u/t < 40?Subtract 40 from both sides of the inequality:
Is 40u/t < 0?Since u and t must be POSITIVE numbers, 40u/t is POSITIVE, which means the answer to the REPHRASED target question is
NO!Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: It took Reiko 20 more minutes to drive from A to B than to make the return trip.Clearly not sufficient
Answer: A
Cheers,
Brent
VIDEO ON REPHRASING THE TARGET QUESTION: