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Math Expert V
Joined: 02 Sep 2009
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From Aqua-Bella island, it is possible to reach Aqua-Marine island by  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 75% (01:32) correct 25% (02:07) wrong based on 82 sessions

### HideShow timer Statistics From Aqua-Bella island, it is possible to reach Aqua-Marine island by either ferry A or ferry B. Ferry A sails 3 hours at 7 kilometers per hour, while ferry B takes a route that is three times longer. If ferry A is slower than ferry B by 2 kilometers per hour, how many hours longer is the journey of ferry B compared with the journey of ferry A ?

A. 4
B. 7
C. 8.6
D. 9.6
E. 12.6

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Re: From Aqua-Bella island, it is possible to reach Aqua-Marine island by  [#permalink]

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Bunuel wrote:
From Aqua-Bella island, it is possible to reach Aqua-Marine island by either ferry A or ferry B. Ferry A sails 3 hours at 7 kilometers per hour, while ferry B takes a route that is three times longer. If ferry A is slower than ferry B by 2 kilometers per hour, how many hours longer is the journey of ferry B compared with the journey of ferry A ?

d = r * t

For A :
dA = rA * tA = 7 * 3 = 21 km

For B :
dB = 3 * dA = 3 * 21 = 63 km
Since, B is faster than A by 2 km/hr
rB = rA + 2 = 7 + 2 = 9 km/hr
tB = 63 / 9 = 7 hrs

tB - tA = 7 - 3 = 4 hrs

Hence, A.
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GMAT 1: 480 Q22 V22 Re: From Aqua-Bella island, it is possible to reach Aqua-Marine island by  [#permalink]

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Ferry A : 3 hrs for 7 km/h
Ferry B : X hrs for (7+2)= 9 km/h

Distance travelled by Ferry A= 7*3= 21 kms
Distance travelled by Ferry B= 3 times longer than Ferry A that is (21*3 kms)= 63 kms

Distance for Ferry B = X hrs * 9 km/hr
Distance is 63 kms from above steps, solving for X we get,

X= 7 hrs

Therefore Ferry B takes (7 hrs- 3 hrs)= 4 hrs longer

A
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From Aqua-Bella island, it is possible to reach Aqua-Marine island by  [#permalink]

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Bunuel wrote:
From Aqua-Bella island, it is possible to reach Aqua-Marine island by either ferry A or ferry B. Ferry A sails 3 hours at 7 kilometers per hour, while ferry B takes a route that is three times longer. If ferry A is slower than ferry B by 2 kilometers per hour, how many hours longer is the journey of ferry B compared with the journey of ferry A ?

A. 4
B. 7
C. 8.6
D. 9.6
E. 12.6

A's rate: $$7$$ km/hour
A's time (given): 3 hours
A's distance, $$D=rt=(\frac{7km}{hr}*3hrs)=21$$ kms

B's rate: B is faster than A by 2 km per hour
B's rate: $$(7+2)=9$$ km/hr
B's distance is three times longer than A's
B's distance: $$(21km*3)=63$$ kilometers
B's time, $$t=\frac{D}{r}=\frac{63km}{9kmh}=7$$ hours

Ferry B (7 hours) takes how many more hours than Ferry A (3 hours)?

$$(7 - 3) = 4$$ hours

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Re: From Aqua-Bella island, it is possible to reach Aqua-Marine island by  [#permalink]

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B Distance is 3 times longer than A
Doesn't it mean total distance is 4 times

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sameeruce08 wrote:
B Distance is 3 times longer than A
Doesn't it mean total distance is 4 times

Bunuel wrote:
From Aqua-Bella island, it is possible to reach Aqua-Marine island by either ferry A or ferry B. Ferry A sails 3 hours at 7 kilometers per hour, while ferry B takes a route that is three times longer. If ferry A is slower than ferry B by 2 kilometers per hour, how many hours longer is the journey of ferry B compared with the journey of ferry A ?

A. 4
B. 7
C. 8.6
D. 9.6
E. 12.6

Source: Economist GMAT

The source is my insertion (per the question's tag).
In other words, however good this question may be, it is not an official question.

sameeruce08 , good catch. You wrote
B's distance is 3 times longer than A's
Doesn't it mean that B's total distance is 4 times that of A's distance?

The phrases "3 times longer than" and "3 times as long as" are hotly debated.*

In this case and similar others, translate "times longer than" with the emphases on times -- on multiplication.
Treat "3 times longer than" as a multiplicative comparison, not as an additive or linear comparison.
B's distance = 3 * A's distance
Why?

1) STANDARD PARLANCE

As KarishmaB notes , native English speakers in standard conversation use "3 times longer than" and "3 times as long as" interchangeably.
The two phrases mean the same thing: whatever A is, multiply it by 3. Here: (my emphasis)
Quote:
Strictly mathematically, three times more would mean 4x but in regular parlance, 3 times older means 3x. So usually, in questions, when people come across 'three time more', they write it as 3x. Hopefully, GMAT will word the questions in a way to avoid this contradiction.

2) STANDARD PARLANCE and INTENDED TRANSLATION

Bunuel concurs here: (my emphasis)
Quote:
Question from GMAT Club member: BUT how can I properly express "1.5 times slower than normal" algebraically???

Bunuel: The wording of the question is not perfect (to say the least).

"Bill drove 1.5 times slower than normal" is intended to be translated algebraically as t(today)=1.5*t(normal), where t stands for time.

3) INTENDED TRANSLATION: ANSWERS give NO OTHER CHOICE

If B were (4 * A), then B's distance would be (4 * 21) = 84 kilometers
B's rate is 9 km/hr. B's time would be 84/9 = 12 hours
A's time is 3 hours.
Time difference between A and B would be (12 - 3) = 9 hours

In other words, interpret "B is 3 times longer than A" as
B is (3 * A)
B = 3A or
B is longer than A by a factor of 3

Maybe one example will make "standard parlance" more understandable:

5 days is 5 times longer than one day.
In one day there are 24 hours. In five days there are 120 hours. 120 = (5 * 24)
The word "times" refers to multiplication.
At the same time, 5 days is also 5 times as long as one day.

I do not recall having seen an official question that presents this issue, but my recall certainly is not definitive.

Hope that information helps.

*The discussion of X is 3 times longer than Y and X is 3 times as long as Y typically follows this course:
• Interpretation #1: longer by a FACTOR
If X is 3 times longer than Y, then X is longer than Y by a factor of 3. The comparison is multiplicative
Y = 10 miles
X = (10 * [factor of] 3) = 30 miles
• Interpretation #2: longer by a DIFFERENCE
If X is 3 times longer than Y, then X is longer than Y by a difference of 3 times the length of Y. The comparison is additive.
Y = 10 miles
X = 10 + (30) = 40 miles

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