A ferry crosses a lake and then returns to its starting point by the

Question

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.

GMATWhizTeam · Answer

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.

mellowmev · Answer

This is a high-quality question and I agree with the explanation

Ashi1204 · Answer

Arey we considering here that the river is still? If not, then first option in inadequate to solve the question.

Posted from my mobile device

ShotaK · Answer

For the statement 2 to be sufficient, should not there be a condition that the ferry never stopped?

quiaitaque · Answer

Bunuel   GMATWhizTeam

I'm not sure if we can use tje average speed formula here, sicme the statemnet 1 says the " ferry’s average speed for the entire round trip is 12 kilometers per hour".

I thought when a statement says "average speed", we cant use the average speed formula; this can only be sued if and only if the term "constant speed" is mentioned.

A similar concept was applied in thsi question;  Shaneice drove nonstop from City X to City Y in exactly 5 hours : Data Sufficiency (DS)

Bunuel · Answer

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.

Average speed is always (total distance)/(total time).

First leg speed = 15 km/h, so one leg = 15t and two legs = 30t.

Statement 1 says that the average speed is 12 kilometers per hour. So two legs combined is 12(t + 3) (since second leg took 3 hours). But the two legs also equal to 30t. So, 12(t + 3) = 30t, which gives t = 2.

A ferry crosses a lake and then returns to its starting point by the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A ferry crosses a lake and then returns to its starting point by the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards