Question

. A container ship is overtaking an oil tanker on the way out of Harwich Harbor, and the first mate notices that if he starts walking from the front of the container ship when the two ships start overlapping, he reaches the back as the two ship separate. He walks at 3 km/hour. If the container ship is 100 m long, and travelling at 12 km/hour, how long is the oil tanker?

Answer 1

The length of the oil tanker is 300 meters

Explanation:

The given parameters are;

The speed with which the first mate is walking = 3 km/hour = 3,000 m/hour

The length of the container ship = 100 m

The speed with which the container ship is travelling = 12 km/hour

The time it takes the first mate to walk from the front to the back of the container,
`t_f` is therefore;

Time = Distance/Speed

`t_f` = 100 m/(3000 m/hour) = 1/30 hour = 1/30 hour × 60 min/hour = 2 minutes

∴
`t_f` the time it takes the first mate to walk from the front to the back of the container = 2 minutes

The resultant speed of the first mate relative to the ground = 12 km/hour - 3 km/hour = 9 km/hour

Given that the first mate starts at the front when the two ships starts overlapping and reaches the back as the two ships separate, we have;

The speed of the oil tanker relative to the container ship = The speed of the first mate relative to the ground

The speed of the oil tanker relative to the container ship = 9 km/hour

The length of the oil tanker = The speed of the oil tanker relative to the container ship × Time of observation of the first mate

∴ The length of the oil tanker = 9 km/hour × 2 minutes = 9 km/hour × 1/30 hours = 3/10 kilometers = 0.3 kilometers = 300 meters

The length of the oil tanker = 300 meters.