Maria bicycles 5 km/h faster than Robert. In the same time it takes Robert to bicycle 60 km, Maria can bicycle 75km. How fast does each bicyclist travel?
m = 5 + r
t = 60/r = 75/m or 60 m = 75 r
so
60(5+r) = 75 r
300 + 60 r = 75 r
15 r = 300
r = 20
then
m = 25
To solve this problem, we need to set up two equations based on the given information.
Let's assume that Robert bicycles at a speed of x km/h. Since Maria bicycles 5 km/h faster than Robert, her speed would be (x + 5) km/h.
Now, we can use the concept of speed = distance / time to connect the distances and speeds.
For Robert, we know that he travels a distance of 60 km, and his speed is x km/h. Therefore, we can write the equation as:
Time taken by Robert = Distance / Speed
t = 60 / x
For Maria, we know that she travels a distance of 75 km, and her speed is (x + 5) km/h. Therefore, her equation is:
Time taken by Maria = Distance / Speed
t = 75 / (x + 5)
Since both Robert and Maria take the same time to travel their respective distances, we can set the two equations equal to each other:
60 / x = 75 / (x + 5)
To solve this equation, we can cross-multiply:
60(x + 5) = 75x
Now, let's simplify and solve for x:
60x + 300 = 75x
300 = 75x - 60x
300 = 15x
Divide both sides of the equation by 15:
300 / 15 = x
20 = x
Therefore, Robert bicycles at a speed of 20 km/h. Since Maria bicycles 5 km/h faster than Robert, her speed would be 20 + 5 = 25 km/h.
Hence, Robert travels at a speed of 20 km/h, and Maria travels at a speed of 25 km/h.