Plane and helicopter

From two airports, a plane and a helicopter took off at the same time. The helicopter was flying to the airport from which the plane took off, the plane to the airport from which the helicopter took off. When they passed each other, the helicopter had flown 100 km less than the plane. The plane flew the remaining distance in 1 hour 20 minutes, the helicopter in 3 hours. Calculate the distance between the airports and the speed of the plane and the helicopter.

Final Answer:

s =  500 km
v₁ =  150 km/h
v₂ =  100 km/h

Step-by-step explanation:

$$\begin{gathered} a=b+100 \\ a+b=s \\ a=v_1\cdot t \\ b=v_2\cdot t \\ s-a=(1+20/60)\cdot v_1 \\ s-b=3\cdot v_2 \\ a=300 \\ b=200 \\ s=500=500\text{km} \\ t=2 \\ {v}_1=150 \\ {v}_2=100 \end{gathered}$$

$v_1=150=150\text{km/h}$

$v_2=100=100\text{km/h}$

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