Two planes leave la at the same time. one heads south, while the other heads north. the southbound plane flies 50 mph slower than the northbound plane. in a .5 hour, the planes are 275 miles apart. what are the speeds

When two planes fly opposite to each other, the rate of separation between them is the sum of the speeds.
Let
S=speed of southbound plane 
then
S+50 mph=speed of northbound plane.
Sum of speeds = S+S+50=2S+50
If the planes are 275 miles apart in 0.5 hours, then
0.5(2S+50)=275
Isolate and solve for S
2S+50=275/0.5=550
2S=550-50=500
S=250 [south bound plane]
The northbound plane flew at S+50=300 mph.