Scooter distance directions

Kate and John set out on their scooters at the same time. Kate rode at a speed of 4.5 km/30 min, and John rode at a speed of 4 km/20 min.

a) How many meters did they travel in 2 minutes if they went in opposite directions?
b) How far apart were they when John rode northeast and Kate rode southeast?

Final Answer:

a =  700 m
b =  500 m

Step-by-step explanation:

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

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

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