Northeast 66694

Katka and Honza rode out on their scooters at the same time. Katka drove at a speed of 4.5 km/30 min, and Honza drove at a speed of 4 km/20 min.

a) how many m did they travel in 2 minutes if they went in the opposite direction?
b) how many miles did they travel when Honza drove towards the northeast and Katka towards the southeast?

Correct answer:

a =  700 m
b =  500 m

Step-by-step explanation:

$$\begin{gathered} v_1=\frac{4.5\cdot 1000}{30\cdot 60}=\frac{5}{2}=2.5\text{m/s} \\ {v}_2=\frac{4\cdot 1000}{20\cdot 60}=\frac{10}{3}\doteq 3.3333\text{m/s} \\ {t}_1=2\text{min}\to \text{s}=2\cdot 60\text{s}=120\text{s} \\ {s}_1=v_1\cdot t_1=\frac{5}{2}\cdot 120=\frac{5\cdot 120}{2}=\frac{600}{2}=300\text{m} \\ {s}_2=v_2\cdot t_1=\frac{10}{3}\cdot 120=\frac{10\cdot 120}{3}=\frac{1200}{3}=400\text{m} \\ a=s_1+s_2=300+400=700\text{m} \end{gathered}$$

$$\begin{gathered} b^2=s_1^2+s_2^2 \\ b=\sqrt{s_1^2+s_2^2}=\sqrt{300^2+400^2}=500\text{m} \end{gathered}$$

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