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 4 km/hour faster than the bicyclist heading south. At 10:15, they are 40 km apart. Find the two bicyclists’ rates.
After they pass at 9PM, they continue traveling for 1.25 hours
So...let the rate of the slower cyclist = R and the faster R + 4
And rate * time = total distance
So.....
Distance traveled by slower cyclist after passing + Distance traveled by faster cyclist after passing = 40 km
So....
R * 1.25 + (R + 4) * 1.25 = 40 simplify
1.25R + 1.25R + 5 = 40
2.50R + 5 = 40 subtract 5 from both sides
2.50R = 35 divide both sides by 2.50
R = 14 k/ hr = rate of slower cyclist
And R + 4 = 18 km/ hr = rate of faster cyclist