S95-34

Official Solution:


We need to know how many minutes, \(t\), it will take for the distance between train A and train B to increase by 2 miles. The trains are moving at different yet constant speeds, and so the difference between their speeds is also constant. This difference is equivalent to the rate at which train B moves ahead of train A, and since \(\text{distance} = \text{rate} \times \text{time}\), or \(d=r \times t\), the distance between the two trains must also change at a constant rate.

Statement 1 says that 3 minutes ago, train A was 1 mile behind train B. Since train A is now 2 miles behind train B, train A must fall behind train B at a rate of 1 mile every 3 minutes. Train A needs to fall behind 2 more miles; that will take \(2 \times 3 = 6\) minutes. Statement 1 is sufficient to answer the question. Eliminate answer choices B, C, and E. The correct answer choice is either A or D.

Statement 2 gives the rates of both trains. Since the trains' speeds are given in miles per hour, we convert them to miles per minute by dividing them by 60, as there are 60 minutes in an hour. Thus, since train A is going 80 miles per hour, it is going \(\frac{80}{60} = \frac{8}{6} = \frac{4}{3}\) miles per minute; similarly, train B is going \(\frac{100}{60} = \frac{10}{6} = \frac{5}{3}\) miles per minute. So, in 3 minutes, train A goes 4 miles and train B goes 5 miles. Thus, train A falls 1 mile farther behind train B every 3 minutes. As we saw in looking at statement 1, this information is enough to answer the question. Statement 2 is also sufficient.


Answer: D