Two cruise ships depart from the same harbor. SeabournOdysseydeparts at 8 AM, and travels due south2 mph faster than the northbound Norwegian Bliss, that left the harbor 1 hour laterthan Seabourn Odyssey. At noon, the ships are 176miles apart. How fast has each ship been travelling?

Velocity is a vector quantity that is specified by both magnitude and direction, such that the relative position of two object moving with known velocities can be determined after a specified

The speed of the SeabournOdyssey is 26 mph

The speed of the Norwegian Bliss is 24 mph

The reason the above values are correct are as follows:

The given parameters are;

The harbor from which the two ships depart = The same harbor

The time Seabourn Odyssey departs = 8 AM

The direction Seabourn Odyssey travels = South

The speed = 2 mph faster than the Norwegian Bliss

The parameters for the second ship, Norwegian Bliss are as follows;

The time of departure = 1 hour later than Seabourn Odyssey

The direction = North wards

The distance between the two ships at 12 noon = 176 miles

Required:

The speed with which each has been travelling

Solution:

Let x represent the speed of the Seabourn Odyssey, and ley y represent the speed of the Norwegian Bliss, we have;

At 12:00 noon, time of travel of the Seabourn Odyssey = (12:00 - 0800) Hours, t₁ = 4 hours

The time of travel of the Norwegian Bliss at 12:00 noon, t₂ = t₁ - 1

t₂ = 4 hours - 1 hour = 3 hours

The distance between the ships, d moving in opposite directions (north and south) is given as follows;

d = x × t₁ + y × t₂

x = y + 2

When d = 176 miles, t₁ = 4, and t₂ = 3, we have;

176 = (y + 2) × 4 + y × 3 = 4·y + 8 + 3·y = 7·y + 8

y = (176 - 8)/7 = 24

The speed of the Norwegian Bliss, y = 24 mph

x = y + 2

x = 24 + 2 = 26

The speed of the Seabourn Odyssey, x = 26 mph

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