Verified answer

D = RT (distance = rate*time)

T = D/R

The problem says, "In that same time," so you know it took Peter to bike 45 km in the same amount or time it took Jodie to bike 63 km. You also know that Jodie was 6 km/h faster than peter, and this is where variables come in to play.

Let x = Peter's time and x + 6 = Jodie's time.

Peter's time is: T = 45/x Jodie's time: T = 63/(x + 6)

REMEMBER their times are equal so you can assume:

45/x = 63/(x + 6)

45(x+6) = 63x

45x + 270 = 63x

18x = 270

X = 15

Now use this number to solve find their rate.

Peter's rate = 15 km/h

Jodie's rate = 15 + 6 = 21 km/h

The main clue from the question is that the times are equal.

The equation distance = rate * time can be rewritten as

time = distance/rate.

You know the distance for both riders, and you are told that Jodie's rate is 6km/h faster than Peter. So if p = Peter's rate, Peter's time is 45/p, and Jodie's time is 63/(p+6).

This gives you the equation 45/p = 63/(p+6).

Cross multiply to get 45 * (p+6) = 63 * p, and solve for p.