At 9:00 on Saturday morning, two bicyclists heading in opposite directions pass each other on a bicycle path.The bicyclist heading north is riding 6 km/hour faster than the bicyclist heading south. At 10:15, they are 42.5 km apart. Find the two bicyclists’ rates.

1 answer

Let's represent the speed of the bicyclist heading south as x km/hour.

Since the bicyclist heading north is riding 6 km/hour faster, their speed can be represented as (x+6) km/hour.

From 9:00am to 10:15am, which is a time span of 1 hour and 15 minutes, the combined distance the two bicyclists travel is 42.5 km.

To calculate their combined distance, we can use the formula: Distance = speed * time.

For the bicyclist heading south, the distance traveled is x * 1.25 hours (since 1 hour and 15 minutes is equal to 1.25 hours).
For the bicyclist heading north, the distance traveled is (x+6) * 1.25 hours.

Adding these two distances together gives us the equation:
x * 1.25 + (x+6) * 1.25 = 42.5

Expanding the equation, we get:
1.25x + 1.25x + 7.5 = 42.5

Combine like terms:
2.5x + 7.5 = 42.5

Subtract 7.5 from both sides:
2.5x = 35

Divide both sides by 2.5:
x = 14

Therefore, the speed of the bicyclist heading south is 14 km/hour, and the speed of the bicyclist heading north is 14 + 6 = 20 km/hour.