Question 1022781
Yes,
{{{a^2+b^2=c^2}}}
Use implicit differentiation with respect to time,
{{{2a(da/dt)+2b(db/dt)=2c(dc/dt)}}}
With 
{{{da/dt=500}}}
{{{db/dt=550}}}
At 2:30, the first plane traveled,
{{{a=(5/2)(500)=1250}}}
The second plane traveled,
{{{b=(3/2)(550)=825}}}
We can calculate c using the Pythagorean theorem,
{{{c^2=(1250)^2+(825)^2}}}
{{{c^2=1562500+680625}}}
{{{c^2=2243125}}}
{{{c=25sqrt(3589)}}}
So then,
{{{2(1250)(500)+2(825)(550)=2(25sqrt(3589))(dc/dt)}}}
{{{1250000+907500=50sqrt(3589)(dc/dt)}}}
{{{dc/dt=(2157500)/(50sqrt(3589))}}}
{{{dc/dt=43150/sqrt(3589)}}}
{{{dc/dt=(43150/3589)*sqrt(3589)}}}{{{mph}}}