Kathy bicycles 5km/h faster than Javier. In the same time it takes Javier to bicycle 49km, Kathy can bicycle 63 km. How fast does each bicyclist travel?
Vk = Vj + 5
Vk/Vj = 63/49 = 9/7
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Vj = (7/9)Vk
Vk = (7/9)Vk + 5
(2/9)Vk = 5
Vk = 22.5 km/h
Vj = 17.5 km/h
awesome. thanks I was trying to do r=d/t and wasn't getting it right.
Kathy bicycles 8 km/h faster than Chris. In the same time it takes Chris to bicycle 57 km, Kathy can bicycle 81 km. How fast does bicylist go?
To solve this problem, we can set up a system of equations based on the information given.
Let's assume Javier's speed is represented by x km/h. Then, Kathy's speed will be x + 5 km/h (as Kathy bicycles 5 km/h faster).
We are given that in the same time it takes Javier to bicycle 49 km, Kathy bicycles 63 km.
Using the formula: Speed = Distance/Time, the time taken by both will be the same.
For Javier: Time taken = Distance/Speed = 49/x
For Kathy: Time taken = Distance/Speed = 63/(x + 5)
Since they both took the same time, we can equate these expressions:
49/x = 63/(x + 5)
To solve this equation, we can cross multiply:
49(x + 5) = 63x
Simplifying further:
49x + 245 = 63x
245 = 63x - 49x
245 = 14x
Now, we can solve for x (Javier's speed):
x = 245/14
x ≈ 17.5 km/h
Javier's speed is approximately 17.5 km/h.
To find Kathy's speed (which is 5 km/h faster), we add 5 to Javier's speed:
Kathy's speed ≈ 17.5 + 5 = 22.5 km/h
Therefore, Kathy's speed is approximately 22.5 km/h.