Elena bicycles 6 km/h faster than Dennis. In the same time it takes Dennis to bicycle 45 km, Elena can bicycle 63 km. How fast does each bicyclist travel?
X = rate of Dennis
X+6 = rate of Elena
time Dennis to travel 45 = time Elena travel 63.
distance = rate x time or
time = distance/rate
45/X = 63/(X+6)
Solve for X = Dennis' speed.
X+6 = Elena's speed.
To solve this problem, we can set up a system of equations based on the given information.
Let's denote the speed of Dennis as "D" km/h and the speed of Elena as "E" km/h.
According to the problem, Elena bicycles 6 km/h faster than Dennis. Therefore, we can say:
E = D + 6 (Equation 1)
We also know that in the same time it takes Dennis to bicycle 45 km, Elena can bicycle 63 km. This means that their times of travel are equal. We can express this as:
time taken by Dennis = time taken by Elena
To calculate the time, we can use the formula:
time = distance / speed
For Dennis, the time is:
45 km / D km/h = 45/D (Equation 2)
For Elena, the time is:
63 km / E km/h = 63/E (Equation 3)
Since the times are equal, we can set Equation 2 equal to Equation 3:
45/D = 63/E
Now, substitute Equation 1 into the equation above:
45/D = 63/(D + 6)
To solve for D, we can cross-multiply:
45(D + 6) = 63D
45D + 270 = 63D
270 = 63D - 45D
270 = 18D
Now, divide both sides by 18:
270/18 = D
15 = D
So, Dennis travels at a speed of 15 km/h.
To find Elena's speed, substitute D = 15 into Equation 1:
E = 15 + 6
E = 21
Therefore, Elena travels at a speed of 21 km/h.
In conclusion, Dennis travels at a speed of 15 km/h, and Elena travels at a speed of 21 km/h.