Let the speed of the bicyclist heading south be \( v \) km/hour. Then, the speed of the bicyclist heading north will be \( v + 4 \) km/hour.
Since they pass each other at 9:00 and are 39 km apart at 10:30, the time elapsed between 9:00 and 10:30 is 1.5 hours.
During this time, the distance traveled by each bicyclist can be calculated as follows:
-
The distance traveled by the bicyclist heading south: \[ \text{Distance}_{\text{south}} = v \times 1.5 \]
-
The distance traveled by the bicyclist heading north: \[ \text{Distance}_{\text{north}} = (v + 4) \times 1.5 \]
The total distance traveled by both bicyclists when they are 39 km apart is: \[ \text{Distance}{\text{south}} + \text{Distance}{\text{north}} = 39 \]
Substituting the distances: \[ 1.5v + 1.5(v + 4) = 39 \]
Simplifying the equation: \[ 1.5v + 1.5v + 6 = 39 \] \[ 3v + 6 = 39 \]
Now, subtract 6 from both sides: \[ 3v = 33 \]
Now, divide by 3: \[ v = 11 \]
Now, we can find the speed of the other bicyclist: \[ v + 4 = 11 + 4 = 15 \]
Thus, the speeds of the two bicyclists are:
- The bicyclist heading south: 11 km/hour
- The bicyclist heading north: 15 km/hour
3 answers