SOLUTION: Jodie bicycles 5km/h faster than Carlos. In the same time it takes Carlos to bicycle 30km, Jodie can bicycle 45km. How fast does each bicyclist travel? Help, how do I solve this

Question 259065: Jodie bicycles 5km/h faster than Carlos. In the same time it takes Carlos to bicycle 30km, Jodie can bicycle 45km. How fast does each bicyclist travel?
Help, how do I solve this kind of problem?
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
This kind of problem can only be solved by prayer and fasting!
You first have to remember the travel formula.
rt=d
rate(speed)*time=distance
First we learn that Jodie (j) is faster than Carlos(c)
j=5+c
Then we learn that carols goes 30 km
c*t=30
And that jodie goes 45 km
j*t=45
in the same time.
Before we set up the final equation , what do we want to know?
Not the time!
But their speeds.
c*t=30
j*t=45
Solve each for t (but didn't I just say we don't want the time.) Be patient there is a method to my madness.
t=30/c
t=45/j
Now we set them equal to each other and t is gone!
30/c=45/j
So now we have one equation with two variables. how is that any better ?
But we have one final trick. did you forget the very first equation?
j=c+5
30/c=45/j
Plug that in for j
30/c=45/(c+5)
Cross multiply
30(c+5)=45c
30c+150=45c
Subtract 30c
150=15c
10=c
j=c+5
j=10+5=15
c=10 kph
j=15 kph

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