Jodie bicycles 6 km/h faster than Peter. In the same time it takes Peter to bicycle 45 km, Jodie can bicycle 63 km. How fast does each bicyclist travel?
If Peter goes p km/h, then Jodie goes p + 6 km/h.
If d = rt, then t = d/r.
We can set up an equation for each of them:
Peter - t = 45 km / p km/h
Jodie - t = 63 km / (p + 6) km/h
Since the times are the same, we can set these equal to each other:
45/p = 63/(p + 6)
45(p + 6) = 63p
45p + 270 = 63p
270 = 18p
p = 15
Thus, Peter goes 15 km/h and Jodie goes 21 km/h.
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Verified answer
If Peter goes p km/h, then Jodie goes p + 6 km/h.
If d = rt, then t = d/r.
We can set up an equation for each of them:
Peter - t = 45 km / p km/h
Jodie - t = 63 km / (p + 6) km/h
Since the times are the same, we can set these equal to each other:
45/p = 63/(p + 6)
45(p + 6) = 63p
45p + 270 = 63p
270 = 18p
p = 15
Thus, Peter goes 15 km/h and Jodie goes 21 km/h.