let

x = the speed of the first train

y = the speed of the second train

the sum of the speeds of two trains is 724.2 miles per hour

x + y = 724.2

the speed of the first train is 5.8 miles per hour faster than then second train

x = y + 5.8

by solving the system of equations

x + y = 724.2

x = y + 5.8

we find

x = 365 mph

y = 359.2 mph

The speed of the first train is 365 mph. The speed of the second train is 359.2 mph.