Maria bicycles 8km/h faster than Dennis. In the same time it takes Dennis to bicycle 33km, Maria can bicycle 37km. How fast does each bicyclist travel?
m = d+8
33/d = 37/m = 37/(d+8)
33(d+8) = 37d
33*8 + 33d = 37d
33*8 = 4d
33*2 = d
d = 66
m = 74
check:
dennis takes 1/2 hour to go 33km
mary takes 1/2 hour to go 37 km
To find out how fast each bicyclist travels, we can set up a system of equations based on the information given.
Let's assume that Dennis's speed is x km/h. Therefore, Maria's speed would be (x + 8) km/h because Maria cycles 8 km/h faster.
The time taken by Dennis to cycle 33 km can be represented by the equation:
Time = Distance / Speed
t = 33 / x
The time taken by Maria to cycle 37 km can be represented by the equation:
Time = Distance / Speed
t = 37 / (x + 8)
Now, since both Dennis and Maria take the same amount of time (t) to cycle their respective distances, we can equate the expressions for t:
33 / x = 37 / (x + 8)
We can solve this equation to find the value of x, which represents Dennis's speed.
To do that, cross-multiply:
33(x + 8) = 37x
Expand:
33x + 264 = 37x
Rearrange the terms:
33x - 37x = -264
-4x = -264
Divide both sides by -4 to solve for x:
x = -264 / -4
x = 66
So, Dennis's speed is 66 km/h.
To find Maria's speed, we can substitute the value of x back into the equation:
Maria's speed = x + 8
= 66 + 8
= 74 km/h
Therefore, Dennis travels at a speed of 66 km/h, and Maria travels at a speed of 74 km/h.