Radio radius

Two friends have shortwave radios with a range of 13 km. The first of them travels by train at a speed of 48 km per hour along a straight section of track, from which the second of the friends is 5 km away. How long will radio friends be allowed for both friends?

Correct answer:

t =  30 min

Step-by-step explanation:

$$\begin{gathered} d=13\text{km} \\ v=48\text{km/h} \\ a=5\text{km} \\ {d}^2=a^2+x^2 \\ x=\sqrt{d^2-a^2}=\sqrt{13^2-5^2}=12\text{km} \\ v=s/t \\ {t}_1=\frac{2\cdot x}{v}=\frac{2\cdot 12}{48}=\frac{1}{2}=0.5\text{h} \\ t=t_1\to \text{min}=t_1\cdot 60\text{min}=0.5\cdot 60\text{min}=30\text{min}=30\text{min} \end{gathered}$$

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