### 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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