saintforlife wrote:
Ashok and Brian are both walking east along the same path; Ashok walks at a faster constant speed than does Brian. If Brian starts 30 miles east of Ashok and both begin walking at the same time, how many miles will Brian walk before Ashok catches up with him?
(1) Brian’s walking speed is twice the difference between Ashok’s walking speed and his own.
(2) If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.
GIVEN: When the men start walking, Brian has a 30-mile lead
Let B = Brian's walking speed (in miles per hour)
Let A = Ashok's walking speed (in miles per hour)
Since Ashok's speed is greater than Brian's speed, the rate at which the gap shrinks = (A - B) miles per hour
For example, if A = 5 and B = 2, then the 30-mile gap will shrink at a rate of (5 - 2) mph.
time = distance/speedSo, time for 30-mile gap to shrink to zero =
30/(A - B)Target question: How many miles will Brian walk before Ashok catches up with him?This is a good candidate for
rephrasing the target question.
distance = (speed)(time)So, the distance Brian travels = (B)(
30/(A - B))
Simplify to get: 30B/(A - B)
REPHRASED target question: What is the value of 30B/(A - B)? Statement 1: Brian’s walking speed is twice the difference between Ashok’s walking speed and his own. We can write: B = 2(A - B)
Expand: B = 2A - 2B
This means: 3B = 2A
So: 3B/2 = A
Or we can say: 1.5B = A
Now take
30B/(A - B) and replace A with 1.5B to get: 30B/(1.5B - B)
Simplify: 30B/(0.5B)
Simplify: 30/0.5
Evaluate 60 (miles)
Perfect!! The answer to the REPHRASED target question is
Brian will travel 60 milesSince we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: If Ashok’s walking speed were five times as great, it would be three times the sum of his and Brian’s actual walking speeds.We can write: 5A = 3(A + B)
Expand: 5A = 3A + 3B
Rewrite as: 2A = 3B
We get: A = 3B/2 = 1.5B
At this point, we're at the same place we got to for statement 1.
So, since statement 1 is sufficient, we know that statement 2 is also sufficient.
Answer: D
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