Kathy bicycles 8 ?km/h faster than Praedup. In the same time it takes Praedup to bicycle 57 km, Kathy can bicycle 81 km. How fast does each bicyclist? travel?

Question

Kathy bicycles 8 ?km/h faster than Praedup. In the same time it takes Praedup to bicycle 57 km, Kathy can bicycle 81 km. How fast does each bicyclist? travel?

Answer 1

Let v be the speed Praedup.
Then the speed of Kathy is (v+8)

In time t, Praedup goes v * t = 57 and Kathy goes (v + 8) * t = 81

(v * t)/((v + 8)*t) = v/(v+8) = 57/81 = 19/27

Cross multiply: 27v = 19(v + 8)
27v = 19v + 152
8v = 152
v = 19 km/hr

Praedup rides at19 km/hr and Kathy at 27 km/hr