Let

v = the rate of the bicycle, v>=0

3v = the rate of the motorcycle

d1 = 450 km the distance the motorcycle travels

t1 = the time of the motorcycle's trip

d2 = 100 km the distance the bicycle travels

t2 = the time of the bicycle's trip

The former requires 2 hours longer to cover 450 km than the latter requires to cover 100 km:

t1 = t2 + 2

Since rate = distance/time we have time = distance/rate

The time of the motorcycle t1 is:

t1 = d1/3v

t1 = 450/3v

The time of the bicycle t2 is:

t2 = d2/v

t2 = 100/v

Plug t1 = 450/3v and t2 = 100/v into t1 = t2 + 2:

450/(3v) = (100/v) + 2

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click here to see the rate of the bicycle calculation

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v = 25 km/h

3v = 3*25 = 75 km/h

The rate of the motorcycle is 75 km/h.

The rate of the bicycle is 25 km/h.