yt and kb are living on contrasting side of a transform boundry. if the plates are moving on the opposed direction at the rate of 2.5cm/year.yt is moving on north wards while kb is moving on southwards.

Question

the current distance along the transform boundry line from kb risidence to yt is 7m
how long will it take for them to be 10m apart?
what will be the distance between the two neighbour in 2045?
what will be the distance between them in 12 years time?

Answer 1

To solve the problem, we need to analyze the situation mathematically. The two individuals, YT and KB, are moving apart at a relative rate due to the opposing directions of the tectonic plates. Given the movement rate is 2.5 cm/year for each person, the relative speed between them is:

\[ \text{Relative speed} = 2.5 , \text{cm/year} + 2.5 , \text{cm/year} = 5 , \text{cm/year} \]

1. Time Taken to be 10m Apart

Currently, the distance between YT and KB is 7 meters. We need to find out how long it will take for them to be 10 meters apart.

We want to increase the distance from 7 meters to 10 meters, which is an increase of:

\[ 10 , \text{m} - 7 , \text{m} = 3 , \text{m} \]

Since we know the rate at which they are moving apart is 5 cm/year, we need to convert 3 meters into centimeters:

\[ 3 , \text{m} = 300 , \text{cm} \]

Now, we can calculate the time required to increase the distance by 300 cm:

\[ \text{Time} = \frac{\text{Distance}}{\text{Rate}} = \frac{300 , \text{cm}}{5 , \text{cm/year}} = 60 , \text{years} \]

2. Distance Between Them in 2045

Assuming the current year is 2023, we have:

\[ \text{Years until 2045} = 2045 - 2023 = 22 , \text{years} \]

In 22 years, at a rate of 5 cm/year, the distance they will move apart is:

\[ \text{Distance} = \text{Rate} \times \text{Time} = 5 , \text{cm/year} \times 22 , \text{years} = 110 , \text{cm} \]

Converting this into meters:

\[ 110 , \text{cm} = 1.1 , \text{m} \]

Adding this to the current distance:

\[ \text{Distance in 2045} = 7 , \text{m} + 1.1 , \text{m} = 8.1 , \text{m} \]

3. Distance Between Them in 12 Years

In 12 years, the distance they will move apart is:

\[ \text{Distance} = 5 , \text{cm/year} \times 12 , \text{years} = 60 , \text{cm} \]

Converting this into meters:

\[ 60 , \text{cm} = 0.6 , \text{m} \]

Adding this to the current distance:

\[ \text{Distance in 12 years} = 7 , \text{m} + 0.6 , \text{m} = 7.6 , \text{m} \]

Summary of Results

1. It will take 60 years for them to be 10 meters apart.
2. In the year 2045, the distance between them will be 8.1 meters.
3. In 12 years (from 2023), the distance between them will be 7.6 meters.