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

Solution:

$$\begin{gathered} s_1=1500\text{ m } \\ {s}_2=600\text{ m } \\ r=v_1:v_2 \\ r=(s_1\mathrm{/}t):(s_2\mathrm{/}t) \\ r=s_1\mathrm{/}{s}_2=1500\mathrm{/}600={\displaystyle \frac{5}{2}}=2.5 \end{gathered}$$

$$\begin{gathered} s_3=90\text{ m } \\ {s}_3=v_2\cdot t_3 \\ {s}_4=v_1\cdot t_3 \\ {s}_4=v_1\cdot (s_3\mathrm{/}{v}_2) \\ {s}_4=s_3\cdot v_1\mathrm{/}{v}_2 \\ {s}_4=s_3\cdot r=90\cdot 2.5=225\text{ m } \\ a=s_4\mathrm{/}{s}_1=225\mathrm{/}1500={\displaystyle \frac{3}{20}}=0.15 \end{gathered}$$

$$\begin{gathered} s_5=60\text{ m } \\ {s}_6=s_5\cdot r=60\cdot 2.5=150\text{ m } \\ c=s_1-s_4-s_6=1500-225-150=1125\text{ m} \end{gathered}$$

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