Bunuel wrote:
A ferry crosses a lake and then returns to its starting point by the same route. The first time it crosses the lake, the ferry travels at 15 kilometers per hour. The ferry’s return trip takes 3 hours. How many hours does the ferry take for the first leg of the trip?
(1) The ferry’s average speed for the entire round trip is 12 kilometers per hour.
(2) The distance the ferry covers to cross the lake once is 30 kilometers.
Solution
Step 1: Analyse Question Stem
• Let us assume that the ferry took t hours for the first leg of the journey.
• Also, let us assume that the ferry’s speed for returning trip be s km/h.
• Ferry speed for the first leg of the trip \(= 15\) km/h
• Time taken by ferry for its return trip \(= 3\) hours.
• Since the ferry crossed the lake and then returned to its starting point by the same route.
o \(15*t = 3*s ……..Eq.(i)\)
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: The ferry’s average speed for the entire round trip is 12 kilometers per hour.
• According to this statement:\( \frac{15*t + 3*s }{ t + 3} = 12\)
• From Eq.(i) and the above equation we can write,
o \(\frac{2*15*t }{t + 3 }= 12\)
\(⟹ 30 t = 12t + 36\)
\(⟹ t = 2\) hours.
Hence, statement 1 is sufficient and we can eliminate answer Options B, C and E.
Statement 2: The distance the ferry covers to cross the lake once is 30 kilometers.
• From this statement, we can write, \(t = \frac{30}{15} = 2\) hours
Hence, statement 2 is also sufficient and the correct answer is
Option D.