SOLUTION: Elena bicycles 6km/h faster than Carlos. In the same time it takes Carlos to bicycle 27km, Elena can bicycle 45km. How fast does each bicyclist travel?

Question 321168: Elena bicycles 6km/h faster than Carlos. In the same time it takes Carlos to bicycle 27km, Elena can bicycle 45km. How fast does each bicyclist travel?
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Elena bicycles 6km/h faster than Carlos.
In the same time it takes Carlos to bicycle 27km, Elena can bicycle 45km.
How fast does each bicyclist travel?
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Carlos DATA:
rate = x km/h ; distance = 27 km ; time = d/r = 27/x hrs
==========================================================
Elena DATA:
rate = (x+6) km/h ; distance = 45 km ; rime = d/r = 45/(x+6) hrs.
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Equation:
time = time
27/x = 45/(x+6)
27x + 27*6 = 45x
18x = 27*6
x = 9 km/h (Carlos's rate)
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x+6 = 15 km/h (Elena's rate)
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Cheers,
Stan H.
============

Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Let Carlos's speed be x mph
Elena bicycles 6km/h faster . x+6 mph
Carlos cycles 27km,
Elena can bicycle 45km. in the same time.
time taken by carlos = time taken by Elena
27/x = 45 / x+6
45x=27(x+6)
45x=27x+162
45x-27x=162
18x= 162
x= 162/18
x=9 mph - Carlos'speed.
15 mph will be Elena's speed.

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