Maria bicycles 7 km/h faster than Carlos. In the same time, it takes Carlos to bicycle 42km, Maria can bicycle 63km. How fast does each bicyclist travel?
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
so now do I have 63x * 42x + 294?
then subtract 63 from both sides and get -21?
then divide 294 by -21?
You don't have an equation!
After you cross-multiply you get
63x = 42x + 294
21x = 294
x = 14
gotcha now, i didn't copy the = sign after 63x... thank you very much!!!
These answers are wrong they both can't be traveling at the same speed and one person be traveling father. Plug the answer 14 back into the original problem they both equal 3.
To find the speeds of Maria and Carlos, we can set up two equations using the given information.
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.