Maria bicycles 6km/h faster than Praedup. In the same time it takes Praedup to bicycle 54km, Maria can bicycle 72km. How fast does each bicyclist travel?
To solve this problem, let's assume the speed of Praedup is 'x' km/h.
Since Maria bicycles 6 km/h faster than Praedup, Maria's speed would be 'x + 6' km/h.
Now, let's calculate the time it takes for Praedup and Maria to cover their respective distances.
The formula for distance is speed multiplied by time: distance = speed * time
For Praedup, his distance is given as 54 km, and his speed is 'x' km/h. So we have the equation:
54 = x * time (Equation 1)
Now, for Maria, her distance is given as 72 km, and her speed is 'x + 6' km/h. So we have the equation:
72 = (x + 6) * time (Equation 2)
We can see that both Praedup and Maria take the same amount of time to travel their respective distances.
Now, let's solve these equations simultaneously to find the value of 'x'.
From Equation 1: 54 = x * time
Divide both sides of the equation by 'x':
54 / x = time (Equation 3)
Now, substitute the value of 'time' in Equation 2:
72 = (x + 6) * (54 / x)
Multiply both sides of the equation by 'x':
72 * x = (x + 6) * 54
72x = 54x + 324
72x - 54x = 324
18x = 324
x = 18
So, Praedup's speed is 18 km/h.
Now let's find Maria's speed by substituting the value of x in Equation 1:
54 = 18 * time
time = 54 / 18
time = 3 hours
From Equation 2: 72 = (x + 6) * time
72 = (18 + 6) * 3
72 = 24 * 3
72 = 72
So, Maria's speed is 18 + 6 = 24 km/h.
Therefore, Praedup's speed is 18 km/h, and Maria's speed is 24 km/h.
Distance = Rate x Time
Maria's rate is t km/hr faster than Praedup.
Maria: (r+6)t = 72
praedup rt = 45
Solve for t in each case:
t = 72/(r+6)
t = 45/r
Since the times are the same the two fractions equal each other. Solve for r.