Let's break down the problem:

Two cyclists start from the same place in opposite directions:

• One cyclist goes towards the North at 18 km/h.
• The other cyclist goes towards the South at 20 km/h.

We are asked to find out after how much time they will be 47.5 km apart.

Solution:

The total distance between them increases as the sum of their speeds, since they are moving in opposite directions. The combined speed is:

$\text{Combined speed} = 18 \, \text{km/h} + 20 \, \text{km/h} = 38 \, \text{km/h}$

Now, we use the formula for time:

$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

In this case:

$\text{Time} = \frac{47.5 \, \text{km}}{38 \, \text{km/h}} = \frac{475}{380} = 1.25 \, \text{hours} = 1 \, \text{hour} \, 15 \, \text{minutes}$

Thus, it will take 1 hour and 15 minutes for them to be 47.5 km apart.

If you'd like more details or have any questions, feel free to ask!

Related questions:

1. If the cyclists' speeds were increased by 5 km/h each, how long would it take them to be 47.5 km apart?
2. What would the time be if the distance they needed to cover was doubled?
3. How would the solution change if one cyclist stopped after half the time?
4. If they start from different points 10 km apart, what would their time to meet be?
5. How far will the cyclists be from each other after 2 hours of riding at their current speeds?

Tip:

When solving problems involving relative motion, always account for whether objects are moving toward or away from each other. The total rate of separation or closure depends on the sum or difference of their speeds.