maria bicycles 8 km/h faster than carlos. in the same time it takes carlos to bicycle 48 km maria can bicycle 72 km. how fast does each bicyclist travel?
carlos' rate ---x
maria's rate --- x+8
time for Carlo to ride 48 km = 48/x hrs
time for Maria to ride 72 km = 72/(x+8)
but their times are equal , so ...
solve 48/x = 72/(x+8)
Distance Speed time
Maria 72 x+8 t
Carlos 48 x t
t=72/x+8
t=48/x
72/x+8=48/x
cross multiply
72x=48(x+8)
72x=48x+384
subtract 48x from both side
24x=384
multiply both side by 24
x=16
x+8
16+8=24
Carlos travels 16 km/h
Maria travels 24 km/h
To find the speed of each bicyclist, let's assign variables to their speeds. Let Carlos's speed be "C" km/h, and Maria's speed be "M" km/h.
According to the information given, Maria bicycles 8 km/h faster than Carlos. So, we can write the equation as:
M = C + 8 ---(Equation 1)
Now, let's use the information that Carlos takes the same amount of time to bicycle 48 km whereas Maria bicycles 72 km. We know that the time taken to travel a certain distance is inversely proportional to the speed.
For Carlos, we can write:
Time Carlos = Distance / Speed = 48 / C
For Maria, we can write:
Time Maria = Distance / Speed = 72 / M
Since both Carlos and Maria take the same amount of time, we can set up an equation:
48 / C = 72 / M ---(Equation 2)
Now, substitute Equation 1 into Equation 2:
48 / C = 72 / (C + 8)
To solve for C, cross-multiply:
48(C + 8) = 72C
48C + 384 = 72C
384 = 72C - 48C
384 = 24C
C = 384 / 24
C = 16
Therefore, Carlos's speed is 16 km/h.
Now, substitute the value of C into Equation 1 to find Maria's speed:
M = C + 8
M = 16 + 8
M = 24
Therefore, Maria's speed is 24 km/h.