Carlos' rate ---> x km/h
Maria's rate ---> x+7 km/h
times are the same :
42/x = 63/(x+7)
cross-multiply and solve for x
Maria's rate ---> x+7 km/h
times are the same :
42/x = 63/(x+7)
cross-multiply and solve for x
then subtract 63 from both sides and get -21?
then divide 294 by -21?
After you cross-multiply you get
63x = 42x + 294
21x = 294
x = 14
Let's assume that Carlos's speed is "x" km/h.
Since Maria bicycles 7 km/h faster than Carlos, her speed would be "x + 7" km/h.
Now, we need to consider the time it takes for Carlos to bicycle 42 km and for Maria to bicycle 63 km.
The formula to calculate time is:
Time = Distance / Speed
For Carlos, the time can be represented as:
Time taken by Carlos = 42 km / x km/h
For Maria, the time can be represented as:
Time taken by Maria = 63 km / (x + 7) km/h
According to the problem, the time taken by both Carlos and Maria is the same. Therefore, we can write the equation:
42 km / x km/h = 63 km / (x + 7) km/h
To solve this equation, we can cross-multiply and simplify:
42(x + 7) = 63x
42x + 294 = 63x
294 = 63x - 42x
294 = 21x
x = 294 / 21
x = 14
Now, we have determined that Carlos's speed is 14 km/h.
To find Maria's speed, we can substitute the value of x back into the equation:
Maria's speed = Carlos's speed + 7 km/h
Maria's speed = 14 km/h + 7 km/h
Maria's speed = 21 km/h
Therefore, Carlos's speed is 14 km/h, and Maria's speed is 21 km/h.