Maria bicycles 5 km/h faster than Carlos . In the same time it takes Carlos to bicycle 30 km, Maria can bicycle 45 km. How fast does each bicyclist travel?

D=R*TIME OR time = distanc/rate.

so set the times equal.

30km/carlosrate=45km/(carlosrate+5)

solve for corlos rate.

can you walk me throught this????

can you help me walk threw this problem?

To solve this problem, we can set up a system of equations using the information given.

Let's start by defining variables for the speeds of Maria and Carlos:
- Let's say Carlos' speed is "c" km/h.
- Since Maria bicycles 5 km/h faster, her speed would be "c + 5" km/h.

Using the formula "distance = speed × time", we can set up the following equations to represent the distances traveled by each cyclist:
1) Carlos: 30 = c × t (equation 1)
2) Maria: 45 = (c + 5) × t (equation 2)

Here, "t" represents the time taken by both cyclists, which is assumed to be the same based on the information given.

Now, we can solve this system of equations:

From equation 1, we can rearrange it to solve for time (t):
t = 30 / c

Substituting this value of time (t) into equation 2, we get:
45 = (c + 5) × (30 / c)

Next, we can simplify the equation:
45 = (30c + 150) / c

To get rid of the denominator, we can multiply both sides of the equation by "c":
45c = 30c + 150

Rearranging and simplifying the equation:
15c = 150

Divide both sides of the equation by 15:
c = 10

So, Carlos' speed is 10 km/h.

Now, substituting this value of c into equation 1, we can find the value of t:
t = 30 / 10 = 3

Therefore, both Carlos and Maria travel at speeds of 10 km/h and 15 km/h, respectively.