kathy bicycles 6 km h faster than javier. in the same time it takes javier to bicycle 33km, kathy can bicycle 45 km. how fast does each bicyclist travel?

k = j+

33/j = 45/k

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that's k = j+6

To find the speed of each bicyclist, let's assign some variables:

Let's say Javier's speed is 'x' km/h.
Kathy's speed is 'x + 6' km/h because she bicycles 6 km/h faster than Javier.

We are given that Javier takes the same time to bicycle 33 km as Kathy takes to bicycle 45 km.

To find the time it takes for each bicyclist, we can use the formula:

Time = Distance / Speed

For Javier: Time = 33 km / x km/h (Equation 1)
For Kathy: Time = 45 km / (x + 6) km/h (Equation 2)

Since the time taken by both bicyclists is the same, we can set Equation 1 equal to Equation 2:

33 / x = 45 / (x + 6)

To solve this equation, we can cross multiply:

45x = 33(x + 6)
45x = 33x + 198

Simplifying the equation:

12x = 198
x = 198 / 12
x = 16.5

Therefore, Javier's speed is 16.5 km/h.

Now, let's find Kathy's speed:

Kathy's speed = Javier's speed + 6
Kathy's speed = 16.5 + 6
Kathy's speed = 22.5 km/h

Hence, Javier travels at a speed of 16.5 km/h, and Kathy travels at a speed of 22.5 km/h.