maria bicycles 8 km/h faster than carlos. in the same time it takes carlos to bicycle 48 km, elena can bicycle 72 km. how fast does each bicyclist travel
Who is elana? I know Carlos, and Maria. Why is elana on a bicycle?
sorry elana is supposed to be maria
Let M be marias rate
C be Carlos rate.
M-8=C
M*time-72=C*time
but time=M/48
putting all that together..
M*M/48 -72=(M-8)*M/48
solve for M first.
-62.2 km/h
To find the speed of each bicyclist, let's assume Carlos' speed is "x" km/h.
Since Maria bikes 8 km/h faster than Carlos, Maria's speed will be (x + 8) km/h.
We know that Carlos takes the same time to bike 48 km as Elena takes to bike 72 km. This means their speeds are proportional.
The equation for time is: Time = Distance / Speed
Let's calculate the time it takes Carlos to bike 48 km:
Time (Carlos) = 48 km / x km/h
Now, let's calculate the time it takes Elena to bike 72 km:
Time (Elena) = 72 km / (x + 8) km/h
According to the problem, Carlos and Elena take the same time to bike these distances, so we can set up the equation:
48 km / x km/h = 72 km / (x + 8) km/h
To solve this equation, we can cross-multiply:
48(x + 8) = 72x
48x + 384 = 72x
384 = 72x - 48x
384 = 24x
Now, divide both sides of the equation by 24:
384 / 24 = 24x / 24
16 = x
Therefore, Carlos' speed is 16 km/h.
Now, let's find Maria's speed:
Maria's speed = Carlos' speed + 8 km/h
Maria's speed = 16 km/h + 8 km/h
Maria's speed = 24 km/h
Hence, Carlos travels at a speed of 16 km/h, and Maria travels at a speed of 24 km/h.