Word equation, algebra one

Question

A northbound train left at midnight. Three hours later, a southbound train left the same station. At 6 a.m. the two trains were 330 miles apart. Find the rate of each train if the northbound train traveled 10 miles per hour faster than rge southbound train.

Answer 1

n = 10 + s

north bound 10 mph faster than south bound

3s + 6n = 330

in 6 hours they're 330 miles apart

3s +6(10+s) = 330

9s = 330-60 = 270

s = 270/9 = 30 mph for 3 hours

n = 10+30 = 40 mph for 6 hours

in 6 hours the north bound went 6x40 = 240 miles

in 3 hours the south bound went 3x30 = 90 miles

for a grand total = 240 + 90 = 330 miles apart in 6 hours