Vacation

Parents are piggybacking their children on vacation to their grandmother and grandfather in a city that is 150 kilometers away. They agreed to meet halfway. Parents will travel at 90 km/h, and grandmother and grandfather will travel at 60 km/h. Parents depart at 12:00 hours. When do grandparents have to arrive at the appointed place simultaneously?

Result

t = 11:35 h

Step-by-step explanation:

$$\begin{gathered} 90x=150/2 \\ 60y=150/2 \\ 90\cdot x=150/2 \\ 60\cdot y=150/2 \\ 180x=150 \\ 120y=150 \\ y=\frac{150}{120}=1.25 \\ x=\frac{150}{180}=0.83333333 \\ x=\frac{5}{6}\doteq 0.833333 \\ y=\frac{5}{4}=1.25 \\ t=12+x-y=12+0.8333-1.25=11.58333=11:35\text{h} \end{gathered}$$

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