### Brain Teasers

# Madadian Ferries

On the great "Chilli" lake of Madadia are two ferry boats that transport tourists from one side to the other.

One boat is the "Lead Balloon", the other is the "Iceberg Magnet". They travel from the Kebab Fountains on the east side of the lake and the Lard Sculpture on the west side of the lake.

Each ferry travels at a constant speed, although the "Lead Balloon" is faster than the "Iceberg Magnet".

The two boats leave from opposite shores at the same time. They pass at a point of 720 yards from Lard Sculptures. Upon arriving at the opposite shore, each boat stays in its slip for 5 minutes, and then starts back. They pass again 400 yards from Kebab Fountains. Assume both boats travel along a straight line. How far is it from Kebab Fountains to Lard Sculptures by water?

One boat is the "Lead Balloon", the other is the "Iceberg Magnet". They travel from the Kebab Fountains on the east side of the lake and the Lard Sculpture on the west side of the lake.

Each ferry travels at a constant speed, although the "Lead Balloon" is faster than the "Iceberg Magnet".

The two boats leave from opposite shores at the same time. They pass at a point of 720 yards from Lard Sculptures. Upon arriving at the opposite shore, each boat stays in its slip for 5 minutes, and then starts back. They pass again 400 yards from Kebab Fountains. Assume both boats travel along a straight line. How far is it from Kebab Fountains to Lard Sculptures by water?

### Answer

Let X = the distance between the two ports. Note that the 5 minutes spent in their slips is irrelevant to solving the problem.The ratio of the distance traveled by the two boats when they pass each other for the first time is: (X - 720) / 720.

The ratio of the total distance traveled by the two boats when they pass each other for the second time is: (2x - 400) / (X + 400).

Since the boats travel at a constant speed, the ratios are equal.

(X - 720) / 720 = (2X - 400) / (X + 400)

(X - 720) * (X + 400) = (2X - 400) * 720

X^2 - 320X - 288000 = 1440X - 288000

X^2 - 320X = 1440X

X^2 = 1760X

X = 1760

Kebab Fountains and Lard Sculpture are 1760 yards apart.

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## Comments

I get 1760 yards, using (2x-400)/(x+400) for the second ratio.

The solution provided (2160 yards) is incorrect as noted by Gizzer. However, there is another correct solution, since we don't know which ferry starts on which side (unless the statement "720 yards near to Lard Sculptures" was meant to imply that they were nearer to Lard Sculptures than to Kebab fountains). If we instead assume that the faster ferry travels 720 yards (while the other goes x-720), and 2x-400 (while the other goes x+400), then you get 720/(x-720) = (2x-400)/(x+400), and x = 1280 yards.

I certainly agree with Gizzer on the 1760 yards. It is about time the Madadian Government stopped paying their Mathematics teachers in Madadian wonks and lured some proper Mathematicians into their schools by including such things as peanuts in their salary package like other nations do.

I do not agree with Gtreqay however. If we assume that the faster ferry travels the 720 yards then 720/(x-720) must be equivalent to (x+400)/(2x-400). The distances must be measured from opposite sides. The answer comes to the same result.

BTW 1760 yards is exactly 1 mile in the old money. It is surprising someone of Mad-Ade's age didn't recognise this immediately.

I do not agree with Gtreqay however. If we assume that the faster ferry travels the 720 yards then 720/(x-720) must be equivalent to (x+400)/(2x-400). The distances must be measured from opposite sides. The answer comes to the same result.

BTW 1760 yards is exactly 1 mile in the old money. It is surprising someone of Mad-Ade's age didn't recognise this immediately.

It took me a bit to see what you were saying, Jimbo, but you are correct. My mistake!

I suppose I haven't been on many ferries. How did we know that they left opposite shores simultaneously? They didn't leave simultaneously for the second trip! I didn't even know they left from opposite shores going opposite directions. I guess I need things spelled out. I didn't get it at all until I read the answer.

I think it would have helped if it had been explicitly stated that the two ferries started from opposite shores at the same time. Being a math problem, there should not be anything assumed. That said, I also get 1760 for the answer.

I agree with the 1760 because of the second ratio correction noted above. To comment on the teaser itself, though, and teasers in general. I think we doers of teasers need to assume the most apparent unstated fact when failure to do so introduces ambiguity. It would be nice if editors were more diligent in adding statements to remove these instances though.

I got 1760, doing it a little differently. I used 720/(x-720) = (x-320)/(x+320), which is the ratio of the first half and second half instead of first half and entire trip.

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