Walker

Walker A takes 3 hours more than B in walking 30 km. If A doubles his speed, he will take 2 h less than walker B. Find the speeds of walkers A and B .

Correct answer:

v₁ =  3 km/h
v₂ =  4.2857 km/h

Step-by-step explanation:

$$\begin{gathered} t_1=3h+t_2 \\ s=30\text{km} \\ {t}_3=t_2-2h \\ s=vt \\ s=v_1\cdot t_1=v_2\cdot t_2 \\ s=2\cdot v_1\cdot t_3 \\ s=v_1\cdot (3+t_2) \\ s=v_2\cdot t_2 \\ s=2\cdot v_1\cdot (t_2-2) \\ {t}_2=7\text{h} \\ {t}_1=3+t_2=3+7=10\text{h} \\ {t}_3=t_2-2=7-2=5\text{h} \\ {v}_1=s/t_1=30/10=3\text{km/h} \end{gathered}$$

$v_2=s/t_2=30/7=4.2857\text{km/h}$

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