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 10:45,
they are 47.25 km apart. Find the two bicyclistsâ€™ rates

I have set the equation like this with x representing one cyclist and x + 5m/s representing the other cyclist's speed. Both their speeds together multiplied by the amount of time which is 1.75 hours will yield the distance they are apart.

Just have to solve for their speeds (x)

(2x + 5)(1.75) = 47.25km

2x + 5 = 27

2x = 22

x = 11

One cyclists speed is 11km/h

The other's is 16km/h since he is going 5km/h faster.