Jodie bicycles 6 km/h faster than Javier. In the same time it takes Javier to bicycle 42km, Jodie can bicycle 60 km. How fast is each bicyclist traveling?
distance/rate=time
60km/(Javier+6)=42km/Javier
60km*J= 42km*J+6*42km
18J=6*42km
Javier speed= 14Km/hr
12km
To determine the speeds of Jodie and Javier, let's use a system of equations.
Let's represent Javier's speed as x km/h. Since Jodie bicycles 6 km/h faster than Javier, Jodie's speed would be x + 6 km/h.
We can use the formula "distance = speed × time" to set up two equations.
For Javier, his distance is 42 km, and his speed is x km/h. So, the equation is:
42 = x × time1
For Jodie, her distance is 60 km, and her speed is (x + 6) km/h. The time taken by both Javier and Jodie is the same, so the equation is:
60 = (x + 6) × time1
Since both equations have the same time, we can solve for time1 by dividing the first equation by the second equation:
42 / (x × time1) = 60 / ((x + 6) × time1)
Simplifying the equation, we get:
42 (x + 6) = 60x
Now let's solve for x:
42x + 252 = 60x
Subtracting 42x from both sides:
252 = 18x
Dividing both sides by 18:
x = 14
So, Javier's speed is 14 km/h. To find Jodie's speed, we can use x + 6:
Jodie's speed = 14 + 6 = 20 km/h
Therefore, Javier is traveling at a speed of 14 km/h, and Jodie is traveling at a speed of 20 km/h.