Answer
$560\ km/h$
Work Step by Step
Step 1. Assume the speed of the plane is $x\ km/h$, the total time for the flight is then $t_1=\frac{420}{x}\ hours$
Step 2. The time her mother takes to drive to the airport is $t_2=\frac{20}{40}=0.5\ hr$
Step 3. Since $t_1=t_2+\frac{15}{60}$, we have $\frac{420}{x}=0.5+0.25=0.75$, thus $x=\frac{420}{0.75}=560\ km/h$
