It takes 8, hours for a 600, km journey,if 12 | vedclass

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(C) Let the speed of the train be $v_t\, km/hr$ and the speed of the car be $v_c\, km/hr$.Case $1$: $\frac{120}{v_t} + \frac{480}{v_c} = 8$  --- $(1)$

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$3:4$

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(C) Let the speed of the train be $v_t\, km/hr$ and the speed of the car be $v_c\, km/hr$.Case $1$: $\frac{120}{v_t} + \frac{480}{v_c} = 8$  --- $(1)$Case $2$: $\frac{200}{v_t} + \frac{400}{v_c} = 8 + \frac{20}{60} = 8 + \frac{1}{3} = \frac{25}{3}$  --- $(2)$Divide $(1)$ by $40$: $\frac{3}{v_t} + \frac{12}{v_c} = \frac{1}{5}$  --- $(3)$Divide $(2)$ by $200$: $\frac{1}{v_t} + \frac{2}{v_c} = \frac{25}{3 	imes 200} = \frac{1}{24}$  --- $(4)$Multiply $(4)$ by $3$: $\frac{3}{v_t} + \frac{6}{v_c} = \frac{3}{24} = \frac{1}{8}$  --- $(5)$Subtract $(5)$ from $(3)$: $(\frac{12}{v_c} - \frac{6}{v_c}) = \frac{1}{5} - \frac{1}{8} \Rightarrow \frac{6}{v_c} = \frac{8-5}{40} = \frac{3}{40} \Rightarrow v_c = \frac{6 	imes 40}{3} = 80\, km/hr$.Substitute $v_c = 80$ in $(4)$: $\frac{1}{v_t} + \frac{2}{80} = \frac{1}{24} \Rightarrow \frac{1}{v_t} = \frac{1}{24} - \frac{1}{40} = \frac{5-3}{120} = \frac{2}{120} = \frac{1}{60} \Rightarrow v_t = 60\, km/hr$.Ratio of speed of train to car $= v_t : v_c = 60 : 80 = 3 : 4$.

It takes $8\, hours$ for a $600\, km$ journey,if $120\, km$ is done by train and the rest by car. It takes $20\, minutes$ more,if $200\, km$ is done by train and the rest by car. The ratio of the speed of the train to that of the car is

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