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From Aqua-Bella island, it is possible to reach Aqua-Marine.

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From Aqua-Bella island, it is possible to reach Aqua-Marine.

by AAPL » Fri Mar 09, 2018 4:49 am
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

The OA is A.

I solved this PS question as follow,

I drew two diagrams:

3 hrs. 7 km/hr
A:-------------->
21 km

7 hrs. 9 km/hr
B:-------------->
63 km

7-3 = 4, answer A.

We have a lot of given information. 3 hrs at 7 km/h for A. This makes a total of 21 km. If B is 3x longer, then the trip for B is 63 km. If A's ferry is 2 km/h shorter, then B's speed is 9. 63/9 gives us 7 hrs for the trip.

Is there a strategic approach to this question? Can any experts help?
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by ErikaPrepScholar » Fri Mar 09, 2018 6:37 am
First thing: the OA for this problem should be A, 4 hours. This means that you solved this question correctly!

You could also do the same math using dimensional analysis for potentially quicker and cleaner work:

$$3\ hours\ A\ \left(\frac{7\ km\ A}{1\ hour\ A}\right)\left(\frac{3\ km\ B}{1\ km\ A}\right)\left(\frac{1\ hour\ B}{9\ km\ B}\right)=7\ hours\ B$$
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by Jeff@TargetTestPrep » Mon Mar 12, 2018 3:49 pm
AAPL 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
Since distance = rate x time, we see that ferry A's route is 7 x 3 = 21 km long. Since ferry B's route is three times longer, ferry B's route is 21 x 3 = 63 km long. Since ferry B is 2 km/hr faster, ferry B's rate is 9 km/hr. Thus, ferry B's time = 63/9 = 7 hours, and that is 4 hours longer than ferry A's time.

Answer: A

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