Question

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 5 km/hour faster than the bicyclist heading south. At 10:30, they are 40.5 km apart. find both of their rates.

Answer 1

Since they are heading north and south, let the southern speed be s, so the northern speed is s+5

After 1.5 hours, the distance is 40.5km

distance is speed * time

40.5 = (s + s+5) * 1.5
27 = 2s+5
22 = 2s
s = 11

so, the cyclist going south moves at 11km/hr, north at 16 km/hr

they are moving apart at 27km/hr, so at 1.5 hours they are 40.5 km apart.