What is the distance between Harry's home and his office?
(1) Harry's average speed on his commute to work this Monday was 30 miles per hour.
(2) If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.
Let
d = distance between Harry's home and his office
Target question: What is the distance between Harry's home and his office?
Statement 1: Harry's average speed on his commute to work this Monday was 30 miles per hour.
To determine the distance (d), we need the travel time.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: If Harry's average speed on his commute to work this Monday had been twice as fast, his trip would have been 15 minutes shorter.
Travel time = (distance)/(speed)
Let v = Monday's speed,
Start with a word equation:
(Monday's travel time) = (travel time at twice Monday's speed) + 15 minutes
Or..., (Monday's travel time) = (travel time at twice Monday's speed) + 0.25 hours
So, we can write d/v = d/2v + 0.25
Multiply both sides by 2v to get: 2d = d + 0.5v
Simplify: d = 0.5v
Divide both sides by v to get:
d/v = 0.5
NOTE: distance/speed = time
[in other words, time = d/v]
So, the Monday's travel time = 0.5 hours
So, statement 2 allows us to determine Monday's travel time, but we don't know Harry's speed.
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that Harry's speed was 30 mph
Statement 2 tells us that Harry drove for 0.5 hours
Distance = (speed)(time)
So,
distance = (30)(0.5) = 15 miles
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
