SOLUTION: Elena bicycles 7 km/h faster than Praedup. In the same time it takes Praedup to bicycle 30 km, Elena can bicycle 51 km. How fast does each bicyclists travel?

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Question 313765: Elena bicycles 7 km/h faster than Praedup. In the same time it takes Praedup to bicycle 30 km, Elena can bicycle 51 km. How fast does each bicyclists travel?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Praedup cycles at x mph.
Elena cycles at x+7 mph.
..
distance traveled by Elena is 51 km.
diatance traveled by Praedup = 30 km.
..
Time taken by Praedup = 30/x
Time taken by Elena = 51/x+7.
..
These two times are same.
..
30/x = 51 / x+7
30(x+7)= 51x
30x+210=51x
21x=210
x=10 km/hr. speed of Praedup
Speed of elena = 17 km/hr