Kathy bicycles 5 KM/h faster than Javier. In the same time it takes Javier to bicycle 57 km, Katy can bicycle 72 km. How fast does each bicyclist travel?
Time = Distance/Rate
x = Javier's rate
x + 5 = Kathy's rate
57/x = Javier's time
72/(x+5) = Kathy's time
Since their time is equal,
57/x = 72/(x + 5)
72x = 57(x + 5)
Solve for x
To solve this problem, let's create variables for the speeds of Kathy and Javier.
Let's say Javier's speed is 'x' km/h.
Since Kathy bicycles 5 km/h faster than Javier, her speed will be 'x + 5' km/h.
Now, let's find the time taken by each bicyclist to cover their respective distances.
The basic formula to calculate the time taken is:
Time = Distance / Speed
For Javier:
Time taken by Javier = Distance / Speed = 57 km / x km/h
For Kathy:
Time taken by Kathy = Distance / Speed = 72 km / (x + 5) km/h
According to the given information, both Javier and Kathy take the same time to cover their respective distances. So we can set up an equation:
57 km / x km/h = 72 km / (x + 5) km/h
To solve this equation, we can cross-multiply:
57(x + 5) = 72x
Simplifying this equation, we get:
57x + 285 = 72x
Subtracting 57x from both sides, we get:
285 = 15x
Dividing both sides by 15, we get:
x = 19
So, Javier's speed is 19 km/h.
To find Kathy's speed, we can substitute this value into the equation we created earlier:
57 km / 19 km/h = 72 km / (19 + 5) km/h
57 / 19 = 72 / 24
3 = 3
Therefore, Kathy's speed is 19 + 5 = 24 km/h.
In conclusion, Javier travels at a speed of 19 km/h, and Kathy travels at a speed of 24 km/h.