Jodie bicycles 5 km/h faster than Robert. In the same time it takes Robert to bicycle 39 km, Jodie can bicycle 54 km. How fast does each bicyclist travel?

I was out of school last week with the flu, and I am trying to do this makeup work but I have no idea how to solve this. I don't need an answer, but if any one can tell me how to solve it I would appreciate it.

Thanks!

J=R-5 where J,R are in km/hr

Time=distance/velocity

distanceJodie/J=distanceR/R
54/J=39/R

54R=39J
then put in for J, (R-5) and you can solve it.

the answer is 12 km/h

To solve this problem, we can set up a system of equations based on the given information.

Let's assume that Robert's speed is R km/h. Since Jodie bicycles 5 km/h faster than Robert, Jodie's speed would be (R + 5) km/h.

Now, let's use the formula: Speed = Distance/Time.

According to the problem statement, Robert bicycles a distance of 39 km in the same amount of time it takes Jodie to bicycle a distance of 54 km.

For Robert:
Speed = R km/h
Distance = 39 km
Time = t (unknown)

So, we have the equation: R = 39/t

For Jodie:
Speed = (R + 5) km/h
Distance = 54 km
Time = t (same as Robert's time)

So, we have the equation: (R + 5) = 54/t

Now we have a system of equations:
1. R = 39/t
2. R + 5 = 54/t

To solve this system, we can use substitution. We can substitute the value of R from equation 1 into equation 2.

Substituting R = 39/t into equation 2, we get:
(39/t) + 5 = 54/t

Next, we can multiply through by t to get rid of the denominators:
39 + 5t = 54

Simplifying the equation, we get:
5t = 54 - 39
5t = 15

Finally, we divide both sides by 5 to solve for t:
t = 15/5
t = 3

Now that we have the value of t, we can substitute it back into either equation 1 or 2 to find the values of R and (R + 5). Let's use equation 1:

R = 39/t
R = 39/3
R = 13

Therefore, Robert's speed is 13 km/h and Jodie's speed is (13 + 5) = 18 km/h.

So, Robert travels at 13 km/h and Jodie travels at 18 km/h.