Glider Motorplane Chase Time

The glider took off from the airport at 10:00 a.m. and flew to the designated destination 102 km away at a speed of 80 km/h. Half an hour later, a motorplane took off behind him at a speed of 180 km/h. When does the motor plane catch up with the glider, and at what distance from the target?

Result

t = 10:54 hh:mm
s =  30 km

Step-by-step explanation:

$$\begin{gathered} 80\cdot (x-10.00)=180\cdot (x-10.5) \\ 100x=1090 \\ x=\frac{1090}{100}=10.9 \\ x=\frac{109}{10}=10.9 \\ t=x=10.9=10:54\text{hh}:\text{mm} \end{gathered}$$

$s=102-80\cdot (x-10.00)=102-80\cdot (10.9-10.00)=30\text{km}$

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