Three roads

The three boys moved from start to finish on three different routes A, B, C, always at the same time. Adam drove road A 1500 m long on a scooter. Blake walked route B 600 m long on foot. Cyril got on a scooter on route C after a 90 m walk, then he left the scooter 60 m before the finish line and reached the finish line on foot. Adam rides a scooter as fast as Cyril. Cyril walks as quickly as Blake. We neglect time losses when getting on a scooter and putting the scooter away. Calculate how many times a scooter ride is faster than a walk. Adam and Cyril started at the same time. Express a fraction of the part of the route that Adam had followed when Cyril mounted the scooter. Calculate how many meters Cyril traveled on a scooter.

Correct result:

r =  2.5
a =  0.15
c =  1125 m


s1=1500 m s2=600 m  r=v1:v2 r=(s1/t):(s2/t)  r=s1/s2=1500/600=52=2.5
s3=90 m s3=v2 t3 s4=v1 t3  s4=v1 (s3/v2) s4=s3 v1/v2 s4=s3 r=90 2.5=225 m  a=s4/s1=225/1500=320=0.15
s5=60 m s6=s5 r=60 2.5=150 m  c=s1s4s6=1500225150=1125 m

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