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The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. Train A leaves New York for Boston at 2 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 2:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York? I) Train B arrived in New York before Train A arrived in Boston. II) The distance between New York and Boston is greater than 140 miles.

The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. Train A leaves New York for Boston at 2 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 2:50 PM and if the combined travel time of the two trains is 2 hours, what time did Train B arrive in New York? I) Train B arrived in New York before Train A arrived in Boston. II) The distance between New York and Boston is greater than 140 miles. Correct Answer Either I or II

Let ‘d’ miles be the distance between cities and ‘x’ mph be the speed of train B

Speed of train A = 100 mph

Combined travel time of the two trains is 2 hours

⇒ d/100 + d/x = 2    ----(1)

An hour later (so at 3:00 PM), Train A passes Train B,

Distance travelled by A in 1 hour (3 PM - 2 PM) = 1 × 100 = 100 miles

Distance travelled by B in 1/6 hours (3 PM - 2:50 PM) = 1/6 × x = x/6 miles

⇒ Total distance between cities = 100 + x/6 = d    ----(2)

Substituting (2) in (1), we get,

⇒ (100 + x/6)(1/100 + 1/x) = 2

⇒ 1 + x/600 + 100/x + 1/6 = 2

⇒ x/600 + 100/x = 5/6

⇒ x2 - 500x + 60000 = 0

⇒ x = 200, 300

Substituting in (2),

⇒ d = 133.3, 150

If x = 200 mph, train A arrives at 3:20, train B at 3:30

If x = 300 mph, train A arrives at 3:30, train B at 3:20

Considering statement I,

Train B reached its destination before train A, hence, arrival time of train B is 3:20 PM

Considering statement II,

⇒ d > 140

⇒ d = 150 miles

Hence, arrival time of train B is 3:20 PM

∴ The question can be answered using either of the statements

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