Kathy bicycles 88 ?km/h faster than Praedup. In the same time it takes Praedup to bicycle 57 km, Kathy can bicycle 81km How fast does each bicyclist? travel?

Question

Kathy bicycles 88 ?km/h faster than Praedup. In the same time it takes Praedup to bicycle 57 km, Kathy can bicycle 81km How fast does each bicyclist? travel?

Answer 1

 

 

distance= Velocity*time

 

If we call V_K  and  V_P the Kathy's and Praedup's bicycle velocities (speeds), we have:

 

V_K = V_P + 88 km/h      Then after a time = t hours, the distance traveled by Kathy is :

 

 D_K = V_K*t  = (V_P + 88)*t   But we already know that after t hours, D_K = 81 km, then:

 

 81 = (V_P + 88)*t   (1)

 

For the same interval of time t hours, Praedup traveled a distance D_P = 57 km, then:

 

 D_P = V_P*t      or    57 = V_P*t   (2)

 

Dividing (1) over (2), we have:  (81/57)  =  (V_P +88)*t / V_P*t)

 

                                                   1.42 =   (V_P + 88)/V_P    

   

Re-ordering termsm we have:   1.42*V_P = V_P + 88     The solution is V_P =  210 km/h      V_K = 210 + 88 =  298 km/h