Two cyclists leave the same park at the same moment and ride along the same route. One travels at 62 km/h, while the other travels at 86 km/h.
After what length of time will the cyclists be 48 km apart?

The correct option is 2 hours.

Step 1: Understand the given information
Speed of the faster cyclist = 86 km/h
Speed of the slower cyclist = 62 km/h
Required distance between the cyclists = 48 km

Step 2: Calculate the relative speed
Because both cyclists leave the same park at the same moment and ride in the same direction along the same route, the rate at which the distance between them increases is the difference between their speeds (relative speed).

$\text{Relative Speed}=86\text{km/h}-62\text{km/h}=24\text{km/h}$

Step 3: Calculate the time taken to be 48 km apart
Using the standard time formula:

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

Substitute the values into the formula:

$\text{Time}=\frac{48\text{km}}{24\text{km/h}}=2\text{hours}$

Therefore, after 2 hours, the cyclists will be 48 km apart.