The posted problem is the virtually the same as the following:
mojorising800 wrote:
If Jim drives at x miles per hour, it takes him 4 hours to travel from A to B. If Tom drives as y miles per hour, it takes him 5 hours to travel from A to B. What is the number of miles between between A and B?
(1) Tom's driving rate is 20% less than Jim's
(2) x + y = 45
Distance from A to B = (Jim's rate)(Jim's time) = (x)(4) = 4x.
If we know the value of x, we can calculate the distance between A and B.
Question stem, rephrased:
What is the value of x?
Time and rate have a RECIPROCAL RELATIONSHIP.
Since the time ratio for Jim and Tom = 4:5, the rate ratio for Jim and Tom = 5:4.
Thus:
\(\frac{x}{y} = \frac{5}{4}\)
Statement 1:This information is given in the prompt:
\(\frac{x}{y} = \frac{5}{4}\) --> \(\frac{y}{x} = \frac{4}{5}\) --> \(y = \frac{4}{5}x = y\) is 80% of x --> y is 20% less than x
Since Statement 1 offers no new information, INSUFFICIENT.
Statement 2:Since we have two variables (x and y) and two distinct linear equations (x/y = 5/4 and x+y=45), we can solve for the two variables.
SUFFICIENT.
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