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[tex]\tt{\huge{\red{Solution:}}}[/tex]
Step 1: Calculate the speed of the car.
[tex]\begin{aligned} s_{\text{car}} & = \frac{d_{\text{car}}}{t_{\text{car}}} \\ & = \frac{\text{600 m}}{\text{2 min}} \\ & = \text{300 m/min} \end{aligned}[/tex]
Step 2: Calculate the speed of the train.
Note: 75 km = 75,000 m
[tex]\begin{aligned} s_{\text{train}} & = \frac{d_{\text{train}}}{t_{\text{train}}} \\ & = \frac{\text{75,000 m}}{\text{50 min}} \\ & = \text{1,500 m/min} \end{aligned}[/tex]
Final Step: Calculate the ratio of the speeds of the car and train.
[tex]\begin{aligned} \text{ratio} & = \frac{s_{\text{car}}}{s_{\text{train}}} \\ & = \frac{\text{300 m/min}}{\text{1,500 m/min}} \\ \text{ratio} & = \boxed{\frac{1}{5}} \: \: or \: \: \boxed{1 \: : \: 5} \end{aligned}[/tex]
Hence, the ratio is 1/5 or 1 : 5
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