Calculate 81492

Jirka went on a moped for a three-day trip.
He drove 90 km on the first day, 30 km on the second day, and 60 km on the third day.
He always drove at the same average speed and always the whole number of hours.
Calculate the average speed if Jirka drove at the highest possible speed.

Correct answer:

v =  30 km/h

Step-by-step explanation:

$$\begin{gathered} s_1=90\text{km} \\ {s}_2=30\text{km} \\ {s}_3=60\text{km} \\ {s}_1=v/t_1 \\ {s}_2=v/t_2 \\ {s}_3=v/t_3 \\ v=s_1/t_1=s_2/t_2=s_3/t_3 \\ 90=2\cdot 3^2\cdot 5 \\ 30=2\cdot 3\cdot 5 \\ 60=2^2\cdot 3\cdot 5 \\ \text{GCD}(90,30,60)=2\cdot 3\cdot 5=30 \\ d=GCD(s_1,s_2,s_3)=GCD(90,30,60)=30\text{km/h} \\ {t}_1=s_1/d=90/30=3\text{h} \\ {t}_2=s_2/d=30/30=1\text{h} \\ {t}_3=s_3/d=60/30=2\text{h} \\ v=d \\ v=\frac{s_1+s_2+s_3}{t_1+t_2+t_3}=\frac{90+30+60}{3+1+2}=30\text{km/h} \end{gathered}$$

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