rohitgoel15 wrote:
Train A leaves New York for Boston at 3 PM and travels at the constant speed of 100 mph. An hour later, it passes Train B, which is making the trip from Boston to New York at a constant speed. If Train B left Boston at 3:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York?
(1) Train B arrived in New York before Train A arrived in Boston.
(2) The distance between New York and Boston is greater than 140 miles.
(A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) Each statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are NOT sufficient.
Please help me know the difficulty level of this question. I was not able to solve it in even 5 mins
Let:
\(d\) be the distance between cities;
\(x\) be the rate of Train B.
"An hour later (so at 4:00PM), Train A passes Train B" --> before they pass each other A traveled 1 hour (4PM-3PM) and B traveled 1/6 hours (4PM-3:50PM).
"Combined travel time of the two trains is 2 hours" --> d/100(time to cover all distance for train A)+d/x(time to cover all distance for train B)=2 --> \(\frac{d}{100}+\frac{d}{x}=2\);
As before they pass A traveled 100 miles (1 hour at 100 miles per hour), then distance to cover for B after they pass is this 100 miles and as B traveled x*1/6 miles before they pass (1/6 hour at x miles per hour), then distance to cover for A after they pass is this x*1/6 miles --> \(100+\frac{x}{6}=d\);
So, we have:
\(\frac{d}{100}+\frac{d}{x}=2\) and \(100+\frac{x}{6}=d\).
Solving for \(d\) and \(x\)
\(d=150\) and \(x=300\);
OR:
\(d=\frac{800}{6}\approx{133.3}\) and \(x=200\).
(1) Says that train B arrived before A.
If \(x=200\) A arrives at 4:20, B at 4:30, not good;
If \(x=300\) A arrives at 4:30, B at 4:20, OK.
Sufficient
(2) Says that \(d>140\) --> \(d=150\) --> \(x=300\), arrival time for B 4:20. Sufficient
Answer D.
P.S. This is definitely a hard (700+) question.
Hope it's clear.
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