\begin{tabular}{l} If Peter travel at \( 100 \mathrm{~km} / \mathrm{h} \) a journey takes 40 minutes. \\ How long does the same joumey takes if he travel at \( 80 \mathrm{~km} / \mathrm{h} \) ? \\ \hline \\ \hline \\ A. 100 minutes \\ B. 50 minutes \\ C. 32 minutes \\ D. 60 minutes \\ Decrease 90 in the ratio \( 2: 3 \)\end{tabular}

To find out how long the journey takes at \( 80 \mathrm{~km/h} \), we first determine the distance. If Peter travels at \( 100 \mathrm{~km/h} \) for 40 minutes, that translates to \( \frac{40}{60} \) hours, equal to \( \frac{2}{3} \) hours. Thus, the distance is: \[ \text{Distance} = \text{Speed} \times \text{Time} = 100 \times \frac{2}{3} = \frac{200}{3} \text{ km} \] Now, to find the time taken at \( 80 \mathrm{~km/h} \): \[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} = \frac{\frac{200}{3}}{80} = \frac{200}{3 \times 80} = \frac{200}{240} = \frac{5}{6} \text{ hours} \] Converting that to minutes gives us \( \frac{5}{6} \times 60 = 50 \text{ minutes} \). So, the correct answer is B. 50 minutes. Now, let's address the ratio problem. To "decrease 90 in the ratio \( 2:3 \)", we can first divide the total ratio into parts. The total parts in the ratio \( 2 + 3 = 5 \). Each part corresponds to: \[ \text{Value of one part} = \frac{90}{5} = 18 \] Now, using the ratio \( 2:3 \), we decrease: \[ \text{Two parts} = 2 \times 18 = 36 \quad \text{and} \quad \text{Three parts} = 3 \times 18 = 54 \] Thus, decreasing \( 90 \) in the ratio \( 2:3 \) results in \( 90 - 36 = 54 \) for the first part, and \( 90 - 54 = 36 \) for the second part.